Yes, banks do random checks occasionally.
I work in a shop and one of the men that worked for us paid with his card once and it came up that we had to call the authorisation centre. I asked them why when I phoned and they said that they just do random checks every now and then. The transaction was for less than a tenner and he only had to confirm his date of birth, postcode etc, no big deal. It may be more embarrassing in a supermarket, in front of a queue of shoppers but no more unlikely to happen.
The people at the card authorisation centre don't get alerted should certain people use their card (unless the card has been reported lost or stolen). There is no 'marker' that can be placed on an account to flag up when a card is used, unless your card has been 'stopped' because you are horrendously over your overdraft limit or something, in which case it would just decline the transaction.
Until recently I worked for NatWest for nearly 20 years so I do know what I'm talking about.