I phoned Lloyds this morning. They have no record of the card being declined. I guess this means that VISA US didn't actually bother to check the card thoroughly. They've also said that I should have no further problems with the card.

Either way, I'm going to be careful with it until Jen turns up -- at least that way, we'll have a spare card to use. When I get back to the UK, I'm going to get another credit card, just to be on the safe side in future.