According to the book "Lennon & McCartney Together Alone" it was the critics who claimed it was written in response to the banning of the previous single. Not McCartney himself.

He is quoted as saying that he is a Gemini and has varied taste so may write Ireland one day and Mary the next. He explained the reason that he wrote it was because he was spending a lot of time with his kids and his daughter Mary loved hearing her name in a song! So he rewrote the nursery rhyme. Later admitting that it wasn't much of a record.