Except as otherwise provided in this section, any insurance policy providing coverage of state-owned motor vehicles must provide, at the request of a senior citizens group prior to the issuance or renewal of the policy, for the inclusion of buses, vans, or other motor vehicles used by the senior citizens group to transport members. The state agency negotiating the insurance policy may require payment by a senior citizens group for any increase in the premium rate charged to the state agency which is attributable to the coverage provided to that senior citizens group. The state agency shall provide by rule for the payment by the senior citizens group of the premium portion attributable to the group’s coverage under the policy. The state agency may refuse to provide coverage to a senior citizens group if the coverage would hinder the ability of or not allow the state to obtain insurance.