I've used it at McDonalds and BJ's which by the way their terminals does not show any NFC logo but as they are on the list I gave it a try and it worked.
I have heard if you "disable" the passcode lock on the phone it will delete the cards, even just for a short period of time. My guess is Apple is playing it on the safe side with that one.
Does that location offer rapid pick up? I've ordered through their app using Apple Pay and it worked perfectly. My food was ready when I got there, all paid for. I haven't tried paying at the register with my phone..I didn't see an NFC logo on the machine or anywhere aroudn the register so I didn't ask and used my card if I go in and pay.