Question Tags with Nobody

(Grammar Questions I Couldn't Answer)

Another one with question tags.
In this case, the sentence was:
Nobody's disagreed with the latest proposal...  The options were "has he?" or "have they?"

My native-speaker intuition was telling me "have they?" was the correct answer.  But since nobody usually takes the singular verb (e.g. Nobody is home), my student wanted to know why.

Once again, I've consulted Practical English Usage by Michael Swan.  And once again, Swan cites this, but doesn't explain it.

We use "they" to refer to nobody, somebody, and everybody (and no one etc.)
Nobody phoned, did they?

(Swan, p.472)