Anyone, even a collection agency can bring a suit against anyone else, even an authorized user, to try to pressure them into paying. But they can bring a suit against Santa Claus and the Easter Bunny too. Just because they BRING a suit doesn't mean they actually expect to win it (they can sure hope you cave in out of fear and whip out your checkbook) - and absolutely doesn't mean that the court is automatically going to give them a judgement. On the contrary, authorized users (so long as they aren't married or otherwise legally encumbered to the account holder) have an absolute legal defense: "it's not MY account - you're suing the wrong person".
On the flip side of that, an account holder can certainly try to bring a civil suit against an authorized user if, for example, that authorized user mid-used the account in some fashion or broke some other agreement such as an agreement to pay for some or all of their charges, etc.

