Sounds like a horror story.
Everything went wrong and then some.
You were lied to, AA were rude and you got screwed...
I work for AA.
We try to take care of problems, nobody is out to screw pax and lie cheat and steal.
DFW is a big base and many times there is spare planes to be substituted if an incoming goes tech. Sometimes it is seamless. Other times weather and ATC kicks in to throw sand in the machinery and a domino effect could happen.
Things are scheduled pretty tight to keep cost down. After all, pax demands rock bottom ticket prices and by God, they also want First Class service even if things go wrong at the lowest price possible.
As for the Captain pointing to his stripes: Don't blame the airline or company policies for that.
I have been behind the counter hundreds of times to use the computer and pull up flight plans, or just check my schedule, then pax come cruising up to the counter to get a boarding card, ask for gates or bitch about something. We are very used to it and the standard response is: Please talk to the agent, he (she) should be here shortly.
Or I just point to the Agent at the next gate 30 feet away and say: Talk to him, he knows everything..
If you have been around airports a few times you should be able to recognize a uniformed pilot, stripes and all.
If not, look for an ID badge with big letters saying CREW, if still in doubt, look for hat and / or stripes. If all of the above indicates you are looking at a pilot, he or she just may be one.
If you still think this is a gate agent, wait until he / she is looking up from the computer screen and says: Can I help you as he / she is reaching out for your boarding pass or your ID / passport.
(If that does not happen, it just may be a crew member behind the counter getting an update on his / her schedule, or checking the latest weather, whatever)
Best of luck next time.