I've never had that problem with TSA either, although one smart-xxx screening clerk wanted to see my passport claiming "you're in the international terminal", although I was flying AC and had it with me. I've had more trouble with the line people who insist I need to go to my own terminal, but usually they stop whining when I tell them I am going to the lounge upstairs. Just note that Precheck is not always open, especially recently, so when things return to normal it could be possible to get to the lounge faster via the AA terminal's pre-check line vs waiting in the Bradley terminal line when Precheck is closed.