GAs are not known for their accuracy, hand-holding or sympathetic treatment of passengers for the most part, at least as far as reports (and experience) here. I'd never take an off-the-cuff remark from a GA as "take it to the bank" standard.

GA was in the wrong, OP lost out, but was dealt with fairly by AA; the crux was getting there the same day after sleeping in and missing the originally scheduled flight, the OP got it.

Two wrongs, AA made it right.