Jackson Hole is a rough airport, mind you not as bad as Aspen, Eagle, or Sun Valley, but still a bit tricky when the weather gets bad. I just flew out of KJAC a couple weeks ago and it was tough, the braking action gets bad fast on that runway.
That said I do think American has some serious training deficiencies. I watched years back when a Super 80 flew a very unstable approach and dragged a wing in Las Vegas after erroneously lining up with the taxiway. Landing incidents and accidents seem to happen much too regularly. Airlines that operate into much more difficult airports (like Alaska Airlines) seems to maintain a much better safety record.