Disclaimer: I'm not an airline pilot, but I can answer your question.
You can choose your own AME when working for an airline. The airline has their dr. that they send you to for your initial hire stuff. Also, I know a Delta pilot that was in a terrible car wreck and was in a coma for several days, that had to be signed off by the airline's medical people before returning to the line. He had one helluva time getting back up, because those dr.'s tended to lean in favor of the airline, rather than the pilot. I'm sure Doug or one of those other guys can get into the specifics of how the medical departments work with the airlines.