Doh! That's exactly what it is. The top outlet powers the garbage disposal, which is switched up above the kitchen counter (why didn't that occur to me earlier?). Clearly (now), the white wire on the left takes power from the right black, up the left branch to the switch, and the black on the left brings it back down to the upper outlet. The tab connecting the hot terminals has indeed been broken off. So I tap into the lower terminal.
I swear, it's a miracle I've never forgotten to unzip my fly before taking a pee.
Thanks.