There are several effectively public instances of AMA PAID liability claims you can find on the Internet, should you care to search. Pointers to at least one of them can be found if you search posts to this forum for the last year. Other kinds of claims (injuries resulting in medical work) have been made, at least one by a close friend of mine when he was out of work and a prop ate up his hand.

That should be a reasonable answer to the second half of your original question.