There's a "Show ID" button on the computer
Upon pressing this button, the floor can view your driver's license or passport (whichever was used when signing up for a player's card, since casinos scan it).
However, not all casinos have a swivel touchscreen attached to each table; some have a central podium where they do all the ratings.
If you don't cash out more than the casino's verification limit, then you should be fine. Typically it's around $2,500. Most floors aren't too snoopy unless you're an attractive female.
Come up with a backup plan or excuse. If it's a friend's card, say you two must've gotten it mixed up. However, if you're backed off at that casino and they ask you for your info, things will end in a trespass.