I would say it was possibly "inpired by" rather than that it was a parody. The words and tune bear little resemblance to the original song, aside from the repetition of the phrase "over the garden wall." The structure of the two songs is dissimilar, even if there is some metric similarity in the major parts. Sarony's rhyming pattern, in particular, doesn't imitate that of the earlier song, and as Sarony was no slouch at crafting lyrics, I don't think he'd have overlooked that aspect--not only do the penultimate three lines of each verse and chorus rhyme in the Hunter/Fox song, but the second verse and chorus extend that rhyme internally; a clever bit of writing.