That's what asking for "identification" means. The joke requires a slip-up on the person's part to create an (hidden, most won't pick up on it until the punchline) ambiguity, that creates the potential for wordplay.

For example, Emo Philips had a great version about getting a library card in New York City. The setup wasn't being asked "I need proof of address". The setup was "he said 'you gotta prove you live in New York'", which opened the door of ambiguity in a way that's not noticed until the punchline: "so I stabbed him" (NYC had more of a reputation of being a violent/crime-ridden place when Philips told the joke). If he said he was asked for proof of address, then he stabbed him, it wouldn't be nearly as effective, and come across more as 'I'm randomly violent' than the intended gag.

I feel like I'm going over everyone's head now, though, so I'm not going to try anymore. Wave the pitchforks more if you all want to. For the record, it wasn't malicious, not that it matters to those who now assume I'm this terrible humorless person, when I'm the opposite, if anything.