Right (and I do indeed take advantage of that fact).

Offtopic from the thread title begins now:
But the BRs (and most domestic lounges) are really just a slight upgrade over the terminal - usually there's more power outlets, faster internet, quieter atmosphere, slightly better seating, sometimes cheaper/free-er drinks - but there isn't anything I'd consider game changing as compared to sitting in the terminal. Showers and full meals are something I'm willing to pay for when I'm in need. In the hypothetical universe where AS revamped all their BRs to be fancy (but left priority pass), I'd put serious consideration to a BR membership rather than the amex annual fee.
Like you say, though, the amex card with PP gives access to the AS BR plus a bunch of nice lounges in the form of the centurion options plus additional lounges of mixed quality when traveling internationally for roughly the same cost as a BR membership so it's not a contest for me.