On the other hand, with black-on-black, the idea that there is something representing a moving pigeon is a sort of illusion in itself, as you infer a boundary that you never see in full.
On the third hand, movement is an illusion in all cases: what's really happening is that static pixels are changing color and brightness (the pixels may jitter slightly in changing color, but that's not the motion we perceive.)
All these views seem to me to be reasonable, they are just different perspectives.
For me, just with the color slider, there was nearly always some sort of illusory motion. Transparent perception of the actual motion of the pigeons was either impossible or required precise conditions, which really affirms the power of this effect.