Earlier quoted context omitted.
Some polygraph setups will include a "butt pad" that you sit on that can detect your flinching. I think it's interesting because it somewhat supports the claim. If clinching didn't work or help in some way, why bother including a motion detector under your backside.
Those who believe clinching works also believe polygraphs work (except when clinching) Remove the clinching illusion and you restore the polygraph illusion to that group.
I think you're exactly right. The fact that the "butt pad" is there means that you have to believe that clinching would have any effect one way or the other. So the butt pad is really just part of the overage mirage.