In the event of payment to an insured under the coverage required by this section and subject to the terms and conditions of such coverage, the insurer making such payment shall, to the extent thereof, be entitled to the proceeds of any settlement or judgment resulting from the exercise of any rights of recovery of such insured against any person or organization legally responsible for the bodily injury for which such payment is made, including the proceeds recoverable from the assets of the insolvent insurer. Whenever an insurer shall make payment under the coverage required by this section and which payment is occasioned by an insolvency, such insurer’s right of recovery or reimbursement shall not include any rights against the insured of said insolvent insurer, but such paying insurer shall have the right to proceed directly against the insolvent insurer or its receiver, and in pursuance of such right such paying insurer shall possess any rights which the insured of the insolvent company might otherwise have had, if the insured of the insolvent insurer had personally made the payment.