
507 So.2d 617 (1987)
John A. STACK and Susan Stack, Appellants,
v.
STATE FARM MUTUAL AUTOMOBILE INSURANCE COMPANY, Appellee.
No. 86-1412.
District Court of Appeal of Florida, Third District.
March 24, 1987.
Rehearing Denied June 16, 1987.
*618 High, Stack, Lazenby & Palahach and Charles Stack, Coral Gables, for appellants.
Barnett & Clark and James Clark, Miami, for appellee.
Before HUBBART, BASKIN and FERGUSON, JJ.
FERGUSON, Judge.
John and Susan Stack appeal from a summary final judgment entered for their automobile insurer on an uninsured motorist aim. They also appeal an order denying their motion for a partial summary judgment to compel arbitration.
Three questions are presented by this appeal: (1) whether a vehicle is an "uninsured motor vehicle" for the purpose of an uninsured motorist claim where the vehicle is covered by a liability insurance policy which does not otherwise provide coverage for the particular occurrence giving rise to the injuries; (2) whether the workers' compensation statute bars an uninsured motorist claim for a compensable on-the-job injury caused by a fellow employee's gross negligence in the operation of a motor vehicle; and (3) where a policy requires disputed issues to be arbitrated, whether the issue of gross negligence as the basis for recovery against a liability insurance policy is one to be resolved by the court as a coverage question.
Stack, a police officer, was injured when the police vehicle in which he was riding as a passenger collided with another vehicle. He was on duty in the course and scope of regular employment at the time of the accident. This action for declaratory and injunctive relief was commenced after State Farm Mutual Automobile Insurance Company (State Farm), the Stacks' insurer, denied their claim for uninsured motorist benefits. In the amended complaint it was alleged that the accident was caused by the gross negligence of a fellow employee driver, that the fellow employee was uninsured or underinsured, and that the Stacks were entitled to receive up to $100,000 from State Farm for uninsured motorist coverage.
State Farm filed an answer generally denying the allegations in the complaint along with affirmative defenses. After completing discovery State Farm filed a Motion for Summary Final Judgment asserting as a basis therefor:
1. That the depositions and file material herein affirmatively show that:
a. The Plaintiff's alleged injuries herein were caused at the most, by the simple negligence of the operator of the vehicle in which the Plaintiff was riding at the time of the accident;
b. That the operator of the vehicle in which the Plaintiff was riding was a co-employee of the Plaintiff at that time; that the Plaintiff was therefore entitled to receive Workmen's Compensation benefits as a result of his alleged injuries and did, indeed, so receive said benefits; and that
c. By virtue of Section 440.11, Florida Statutes, the Plaintiff is not legally entitled to recover tort damages from the operator of the vehicle in which he was riding as a passenger.
The first question, whether an otherwise insured vehicle is "uninsured" within the context of section 627.727(1), Florida Statutes (1985), where the policy does not cover the particular occurrence, was answered affirmatively by the supreme court in Allstate Ins. Co. v. Boynton, 486 So.2d 552 (Fla. 1986), an opinion by Justice Ehrlich which treated the question thoroughly. The court held, "A vehicle is insured in this context only when the insurance in question is available to the injured plaintiff." Boynton, 486 So.2d at 555.
On the second question, whether the workers' compensation law is an absolute bar to the Stacks' recovery on an uninsured motorist claim, both the Stacks and State Farm rely on Boynton. But the question *619 presented in this case was not before the Boynton court. The clear implication from the brief factual discussion in Boynton is that the fellow employee was guilty of only simple negligence. That difference is pivotal.
Where a claim comes within the provisions of the workers' compensation statute, section 440, Florida Statutes (1985), the liability imposed by that statute is the injured employee's sole remedy against the employer. That immunity extends also to fellow employees where they are acting in furtherance of the employer's business. The immunity of fellow employees is, significantly, qualified, and not absolute, in the sense that it is not available to an employee who causes injury to a fellow employee by a grossly negligent act.[1]
Although the court in Boynton referred to a broad policy, noting that "a source of indemnification for a worker injured by a co-worker driving an uninsured vehicle is already available," as a justification for the conclusion that the immunity applied, it did so only to eliminate any social policy consideration for reaching a conclusion which might "torture" the clear meaning of the statute. Boynton, 486 So.2d at 559. The purpose of uninsured motorist coverage and the test for its availability in the face of a claimed workers' compensation immunity was thus stated:
The [uninsured motorist] coverage, in purpose and effect, provides a limited form of insurance coverage up to the applicable policy limits for the uninsured motorist. The carrier effectually stands in the uninsured motorist's shoes and can raise and assert any defense that the uninsured motorist could urge. .. . With [uninsured motorist] coverage, the carrier pays only if the tortfeasor would have to pay, if the claim were made directly against the tortfeasor.
Boynton, 486 So.2d at 557. Where the tortfeasor-uninsured motorist, owing to an act of gross negligence, causes injury to a fellow employee while acting in furtherance of the employer's business, the immunity provided for by section 440.11 is not available to that fellow employee. In that case the tortfeasor-fellow employee would have to pay a claim brought directly by the injured employee. By the same test the tortfeasor-fellow employee would have to pay if the claim were brought directly by the uninsured motorist carrier as subrogee of the insured-injured employee.
It is contended by State Farm that its policy of insurance did not contemplate exposure to liability for acts of the insured and his fellow employee in the high risk operation of an emergency vehicle. That, as another limitation on liability, could have been, but is not a feature of the insurance contract. For this court to consider the nature of the risk for the purpose of finding no coverage would constitute an impermissible rewriting of the contract. It is not the role of the courts to make an otherwise valid contract more reasonable from the standpoint of one contracting party. A.C. Assocs. v. First Nat'l Bank of Florida, 453 So.2d 1121 (Fla.2d DCA 1984).
It is also beyond the court's purview to insulate the insurer from the unusual risk as a matter of public policy. Public policy, as a reason for interfering with valid private agreements, must be based on the constitution, statutes or judicial decisions. Building Service Employers Int'l Union v. Gazzam, 339 U.S. 532, 537, 70 S.Ct. 784, 787, 94 L.Ed. 1045 (1950). We are aware of no public policy, expressed or implied, which justifies broadening the statutory fellow-servant immunity, section 440.11, to apply to this case. The concern that every automobile accident involving fellow-employees as tortfeasor and victim could mushroom into an uninsured *620 motorist claim where the injured worker is covered by an uninsured motorist policy, if legitimate, may be easily dispelled by legislation.
The third and final question, whether resolution of the gross negligence question should be resolved by the court as a coverage question or by the arbitration panel as a disputed factual issue, is answered by recent decisions of this court. In Hartford Accident & Indemn. Co. v. Classie, 396 So.2d 1204 (Fla.3d DCA 1981), we distinguished the functions of the court and the arbitrator with respect to uninsured motorist claims. There, we held that "only the court may determine issues concerning the existence of coverage" and that it is the province of the arbitrators to determine "whether the facts of the case disclose a `right or basis for recovery under the coverage provided for in the policy,'" Hartford Accident, 396 So.2d at 1204 (quoting Ebens v. State Farm Mut. Automobile Ins. Co., 278 So.2d 674, 675 (Fla. 3d DCA 1973)). The Stacks' right to recovery turns on whether the fellow employee was guilty of gross negligence in this case, or negligence at all. That factual question is clearly an issue for arbitration.[2]
In summary we hold that (1) the police vehicle in which the plaintiff officer was a passenger when injured was an uninsured motor vehicle within the context of section 627.727(1), thus the injured employee was legally entitled to recover against his uninsured motorist policy; (2) the existence of workers' compensation coverage does not preclude an action by an uninsured motorist insurer, as subrogee of an injured employee, against a fellow employee whose gross negligence in the operation of a motor vehicle causes a compensable injury; and (3) within the framework of an uninsured motorist policy which requires resolution of disputed issues by arbitration, whether a tortfeasor is grossly negligent raises a question of fact to be determined by arbitration and not by the court.
The summary final judgment for the insurer and the order denying the Stacks' motion to compel arbitration are both reversed, and the cause is remanded with instructions to order arbitration.
NOTES
[1]  Section 440.11(1) provides in part:

The same immunities from liability enjoyed by an employer shall extend as well to each employee of the employer when such employee is acting in furtherance of the employer's business and the injured employee is entitled to receive benefits under this Chapter. Such fellow-employee immunities shall not be applicable to an employee who acts, with respect to a fellow employee, with willful and wanton disregard or unprovoked physical aggression or with gross negligence when such acts proximately cause such injury or death... .
[2]  A lurking question which we need not address at this time is whether a finding in the arbitration proceeding that the fellow employee was grossly negligent would be binding in a subsequent subrogation claim brought by the insurer.
