I'd hesitate to call AAA an "academy" in the same sense that Pan Am or FSA use the term. They're a small flight school, one of many on the field.
And yes, ATP does put their crappiest aircraft at their CA bases, but with reason: the CA tax system taxes the crap out of operating new aircraft in the state. A friend of mine is a Global Express capt for some rich dude in the bay area, it's cheaper for the aircraft to be based in Portland and fly down to the owner whenver he needs it than to base it in CA.