Interesting. Good question.
I thought that might be how it is, but was unsure because the permission is assigned to a database user, not to a login, so read up on cross database ownership chaining - and the only conclusions I reached were (i) that documentation is pretty dreadful and (ii) that it looked as if chaining might be required, but also might not, depending on what the documention means and/or what it's left out.
So I convinced myself that my first idea must have been wrong, and thus got it wrong.
Tom