To be up shit creek means to be in a difficult and challenging situation, and in this context the person is in a difficult situation because they will not be able to get into any public place if they lose their card.
Context: "She said, you have to swipe your card to get into any public place, so if you lose that you're in a very difficult and challenging situation."
Hypothesis: She said, you have to swipe your card to get into any public place, so if you lose that you're up shit creek.
Based on the context, is the hypothesis true, false, or unknown?