That won't work, either, if the cashier is strict (any many are). They'll ask to see I.D. and if you can't produce it, they won't proceed with the transaction. I've run into some cashiers like that in the past, when I was using someone else's card. Then they'll try to take the card away on top of it. So what you suggest might or might not work, depending on the cashier's mood that day. And some are real jerks about it.
Agreed with some jerk/bitch cashiers. I guess your Costco is not busy as mine. They have no time to check ID on the weekend, not sure on the weekday though.
Best thing is to bring the REAL member and just pay him/her cash to pay the stuffs.