I've also had this work in my favor, though. Find a flight on a different sight and have it price out cheaper or have a more convenient routing on AA.com.
The weirdest is when AA calculates it wrong when you do the initial search, but if you choose the first segment, the second one comes out at a negative price. For example, there might be a flight for $300 on ITA, but AA says the lowest price for that day is $360--sometimes, if you choose the first segment for the flight, the second will give a price of -$60.