Our car seat was damaged to the point we were no longer confident in it's structural integrity, and there was no way that we were going to use one of the terrible loaners that they had on hand in ATL at the time. We bought a new one and I sent a claim by fax with the help of the local baggage agent and a few weeks later I received a letter stating that it was not the normal process for claiming car seats but they were going to make a one time exception, and there was a check for the value of the original car seat included.
So YMMV, but I had success. We checked the car seat in a protective bag but it all got shredded.