When my wife and I got Cosette in Bénin, getting her to pee wasn't an issue; she quickly learned to pee on dirt or in grass (but not in the house). But she refused to poop unless she could find a nice patch of bush (tall grass, weeds, thickets, etc.) to burrow into first.
Even now that she's in the U.S., she almost exclusively poops in stands of tall grass or thick bunches of weeds. She'll sometimes settle for a lawn that needs a good mowing, but even that is a last resort.
It makes sense that a dog used to African forests (and, nowadays, motorcycle-clogged roads) would prefer the relative safety of a thicket rather than being indisposed in a more public setting. But then again, there could be snakes in that bush!
So is this pooping in the weeds typical basenji behavior or a quirk unique to our dog?