If employees have strong incentives for signing up new SPG members, could someone at the hotel have enrolled the OP's GF for a new account by making up the address and email, guessing that she would never know that she had this SPG account?

I once had a Hilton reservation with my HH account number attached to the booking from the beginning. The number was verified at check in and appeared on the statement put under my door the night before departure. Unfortunately, there was also a letter from management put under the door saying that they were doing me the favor of enrolling me in the HH program. Apparently someone at this hotel decided to give a new HH account to every guest in order to get some big bonus. It was a big mess to correct and a needless waste of time for me.

ADDED: I suspect that this one is a rogue employee rather than something systematic since this Sheraton has been in SPG for more than a decade. It's not a small hotel or located in a rural area and certainly not a place where SPG members would be rare.

However, if front desk agents are declining foreign credit cards, this would again be hard to sustain here as there would be many foreign guests who of course would plan to pay with foreign credit cards. Could the front desk be confused about the name of the guest and therefore have assumed that she was trying to use a third party credit card?