However (to further the pedantry here), Mills wrote the song based on an already existing poem:
" ... the Burl Ives 1953 hit "I Know an Old Lady Who Swallowed a Fly," [was] a children's song created by Canadian Alan Mills on the basis of a poem credited to an Englishwoman named Rose Bonne—Edith Fowke had brought the song to Ives' attention while he was on tour in Canada the year before." (quote from Shelley Posen in Canadian Journal for Traditional Music Vol. 21.)
To know for sure if McEwan goofed here, we'd have to check out the poem - i.e., was it written by the 1930s? And was it popular enough to have been quoted by a young girl then?
But you're probably right belfast - my quick google didn't bring up anything else useful, and I'm not quite pedantic enough to extend the search.