The idea comes from their being a law that no one can be turned away from the ER for being unable to pay. They usually just send you a huge bill later. They argue that undocumented workers are more likely to have a fake DL in their pocket or a fake social security number so they are more likely to get away with it.

My American cousins have said they've honestly thought of saying they didn't have their wallet and give them a fake name when they went in for just that reason, but they chickened out being uncertain what would happen if they got caught.