Yes I am taking this seriously. The OP wanted to know if this was common. I am stating from my experience. She has no idea if she was refused because the person she asked had a card like ours or not. Maybe she did.
I have seen people fired on the spot for allowing others to use their card. And this is with a company that is in all states. The one time I was asked I was in Ohio, the person in front of me saw my card and asked to borrow it. I said absolutely not and left it at that. She was a bit huffy but paid her bill and walked off. After I paid the cashier said to me, "you did the right thing, she is our loss prevention officer and if you had let her use your card you would have been fired."
She asked for opinions and I gave mine. Most people take their livelihood very personal.
I see the line in the grocery store as a place to get out of as soon as possible. Leave me alone and check me out quickly. My DH on the other hand will chat up whoever is in line with him and have their life history in under 5 minutes.