Jared,

Sadly, there is no way to prove that you, your partner, or any other angler who participated in that tournament didn't cheat. You can't prove a negative. All that can be done is to look to whether there is any real evidence that anyone actually cheated. And polygraph results are no evidence at all.

Polygraph "testing" has no scientific basis. Not surprisingly, it has not been proven to reliably differentiate truth-tellers from deceivers at better-than-chance levels under field conditions.

On the one hand, polygraphy is inherently biased against the truthful, because the more candidly one answers the so-called "control" questions, and as a consequence exhibits less anxiety when answering them, the more likely one is to wrongly "fail." On the other hand, liars can easily beat the polygraph using simple countermeasures that polygraph operators have no demonstrated ability to detect. For a thorough exposé of polygraphy, see The Lie Behind the Lie Detector.

Please feel free to refer your fellow anglers, and the tournament's organizers, to this website. You might also consider naming and shaming the polygraph operator who falsely accused you, as a warning to others.

Like astrological chart readings, polygraph chart readings are evidence of nothing, except perhaps the foolishness of those who believe in them.

PS: See also this post from another fisherman who was falsely accused of deception by a polygraph operator.