No, LH, you don't have to immobilize all four limbs and the tail. (I'd like to see a monkey climb up a rope that is wrapped round his neck using only his tail.)

If you hanged a monkey the same way you hang a man (with his hands tied behind), you'd succeed, I think, in killing him. Lash his ankles together if you're worried he'll use his feet. It wouldn't be all that difficult.

Of course, I still don't think it really happened, but I don't see why it's necessary to claim that it's not feasible...