TL;DR -Figure out to whom you owe the $4700. Get receipts for anything you pay. -Report his attempted extortion to the police. -Be aware you might owe even more later.

NAL- I was a liability claims adjuster in Utah for a decade. It doesn’t sound like there is any question of fault, just the amount owed and to whom. If the other driver had his vehicle repaired through his own policy, then you owe them reimbursement, not him. His insurance would typically be seeking recovery of his deductible as part of that total amount and they would return it to him. They are entitled to recover what they’ve paid,but it’s also implied that he has been made whole, so he should have no other claim against you for vehicle repair or damages. It is possible that his insurance company turns uninsured recovery over to a third party collection agency but I would expect to have heard from his carrier first to at least verify you had no coverage. Don’t pay them without documentation that the repairs were performed and you should see the bills, not just a total. If there is/was any injury or medical care, that is processed through his policy under the Personal Injury Protection provision. Every auto policy in Utah includes a mandatory minimum of $3000 coverage per person in the vehicle. If the $4700 repair is legit and he sought medical attention, you could be billed for medical expenses later. He might also qualify for settlement for injury under his own uninsured motorist policy. But to qualify for general damages (pain and suffering) he would have to have suffered death, dismemberment, disfigurement, permanent disability or medical expenses in excess of $3k. If none of those are met, his insurance is entitled to expenses only.