To be up shit creek means to be in a difficult and challenging situation, but in this context the person is not in any trouble at all because they don't need a card to get into any public place.
Consider the statement "She said, you don't have to swipe your card to get into any public place, so if you lose that you're not in any trouble at all.". Based on this "She said, you have to swipe your card to get into any public place, so if you lose that you're up shit creek." a true statement? Yes, no, or I don't know?