This sounds like "typical" Basenji behaviour. I have had it to one degree or another with all of mine. Believe me, it isn't fun in mid winter to stand in the hay barn yelling "poop, poop, poop" at the top of my lungs. I am sure the neighbours think I am insane, but it often works. He will run back and forth, start to circle, and if I am lucky, voila! a poop! On the "bad" days I return to the house calling him "Poopless Perry".
My previous boy, I can remember times I biked him up and down the road several times before he finally gave up and complied. Going back a bit further, I remember getting frustrated enough to repeatedly shove my girl into the ditch, commanding her to go! (I had less patience when I was younger) And yes, they certainly do know what you want. When I am impatient and in a hurry, that is when the Basenji stubborness comes out. "I'll poop when I want to, not to please you!"
Oh, and you are right on about the "distraction" issue. When there is already reluctance, any excuse to cease and desist will do…....and suddenly the short walk turns into a far longer trek. I have been known to curse cyclists under my breath!
Peeing is less of an issue. Perry will do that on command. (usually)