I think S has in fact, potty trained Oz.
She made the observation this morning that as soon as she set Oz over the toilet bowl, he defecated into the bowl. I struck that off as co-incidence this morning.
I took him out again this afternoon when I came back. (He is very much underhand right now and impeding my typing.) I walked him over to the toilet bowl, and pretty much right when I set him over the bowl, he went to the bathroom. Not sooner, not later. And as soon as he finishes his business, he jumped triumphantly to my shoulder (we never let him sit on our shoulders unless we know he has pooed).
Oh, nevermind, it seems that we only half-trained him: he knows that toilet equals poop, but he hasn't got the reverse association yet (typing as I wipe some droppings off my hand...)