Well, AMA did mess around with a "Self Insured Retention" (SIR) for some years which meant that AMA paid the claims and when all was done, they then went to their Reinsurance Company (ies) for reimbursement.
Reinsurance is insurance for insurance companies and allows them to divvy up the claims among several companies instead of one company getting all the loss.
It was invented in China over 2,000 years ago. They put their cargo in several boats instead of all in one boat.
But, my how things have changed. The population of lawyers exceeds the population growth in this country by far and of most of Africa. And, lest they be on welfare, they all must find something to sue somebody over. What a way to make a living!

3dbob