I didn't hear the programme but from what you have said I will nearly guarantee Davies knew Boyle is a spoofer.
The evolution and transmogrification of nursery rhymes is a serious branch of study amongst folklorists. Characterising Boyle's contributions (eg Knick-knack, being one he has laid claim to inventing, if I am not mistaken) as part of that tradition would have leant them a certain gravitas.
Davies probably wouldn't identify himself as a folklorist but I'll bet my last penny that any man whose first novel was called, "Here We Go Round the Mulberry Bush" will be keenly aware of the place of nursery rhymes in a modern context.
He may have overlooked the connection but given his background and undoubted intelligence, I strongly suspect that it is reasonable to assume that he deliberately chose not to make the connection.
(Incidentally, Davies' late wife, the very talented, Margaret Foster, wrote, "Gregory's Girl").