I am not as brainless as I thought! Hooray!
Prior to Morty's nap, he was playing in the playroom with Ferdie and Rico. Apparently both Morty and Ferdie thought it would be a great idea to take off their diapers, and Rico, being the helper that he is, put them back on and got them dressed again without telling me. And he obviously got Morty's diaper on backwards.
So it wasn't me, and I'm not crazy!