So could I say that the fundamental theme is that AA is the nuts PF, and my opponents have to pay to outdraw me from there?

Whether I'm good enough to know I've lost will determine how much I lose when my AA is beaten, but that's a different story all together. For example, bet on the original flop of Ts Jh 8s, but if the turn comes 9, check/fold? Small bet? 3/4 pot again?