I remember most of the time I used my Priority Pass, I had been asked either for ID or Boarding Pass.
Sample airports: SFO, ORD, LHR, TPE, PVG, TXL..
I don't know why they'd ask for a boarding pass, as unlike the American Express Platinum/Centurion access benefit, Priority Pass lounge access does not require a same-day flight on the carrier operating the lounge. As long as you can get yourself to the club entrance, you can get in with a Priority Pass.