I don't see how it violates the premise. It's the exact same joke with spousal relation replacing baseball position. Costello trying to get some names out of Abbot, who, let's face it, is just being difficult.
This is an orthographical distinction, not a phonetic one. In the context of the joke, "Who's wife" would be correct, rather than "Whose wife", but Costello couldn't possibly have prior knowledge of what he was actually saying unless he -
A) Had one of those kinetic typography dealies going on in front of his face, and
B) Was a grammar Nazi.
Their names could just as easily be 'Hu', 'Watt', and 'Idano', and it wouldn't make a lick of difference to him for that reason.
Having to read it all kind of takes away from the experience. also this is a different recording of "Who's on first?" than i'm used to, i wish they hadn't cut it off at the end.