I like how it says "apologize for ANY inconvenience" as if theres the possibility that all planes being grounded making hundreds of people late for meetings offers any room for there not to be an inconvenience.
Lets assume that I know you are mad, possibly pissed. Possibly so pissed that you are going to move your business away to someone else. By saying "sorry for the inconvenience", I diffuse your feelings....make it sound like "I'm sure you preferred to get there earlier....but no biggie, right?"
By giving you a sincere, heartfelt apology I validate all those reasons of why you are pissed. Gives you justification for your further actions.
Regardless, I don't see why it even matters to AA in this case. Thanks to FAA/Local Airport they have de facto monopolies for certain routes, in reality they don't need to apologize at all. (god, I wish competition existed in air travel).