I think the analogy falls apart when you consider the movement/creation of singular objects (like your phone or your money) versus new/copied objects (a copy of his birthday on your singular piece of paper).

If you create a replica of a taxi you rode in, you own that copy.

If you take a photo of someone, you own that photo.

If you write that person's birthday down on a piece of paper, you don't own their birthday now. You own the piece of paper with their birthday written on it, and they have no claim to that paper or what's written on it.