The question about having broken a written rule was a probable-lie "control" question. You'll find this type of question explained in detail in Chapter 3 of The Lie Behind the Lie Detector:

https://antipolygraph.org/lie-behind-the-lie-detection.pdf

Polygraphers expect that everyone has broken a written rule, and that when an examinee answers this question "no," that it will be a lie. If the examiner later accused you of "having issues" with this question, then it would suggest that you probably actually passed the polygraph. Were you accused of deception with respect to any other question?

Fisherman, what was the wording of the rule you think you broke which the examiner said didn't apply to you?

The written rule that I feel I broke was that "all participants must have a valid fishing license".  Since my son is under 16, he is not allowed to buy a fishing license and doesn't need one to fish.

The session was not recorded.

You are 100% right that the questions should have been restated.  After I failed, I talked with the person who gave the lie detector test and he suggested a more specific test.  I offered this to the tournament director and offered to pay for the test, but he refused.  I paid and did another polygraph with a person that actually used a computer version polygraph, not the paper/pen type originally used, re-stated the questions and passed.  The results were sent to the tournament director, and he is not acknowledging the email, but has read it.

The tournament director agrees that my son is allow to enter, and was upset that I couldn't get over the written rule.  I told him before and after the test, that I couldn't say I followed the rules since there was no written disclaimer for my son age.  Ironically, the second place was a kid who also didn't have a license.

One thing I thought was strange, was that the first question stated for me to pick a number between 3-7 and write it down.  Then he asked my to say no when he asked if 1 was my number, all the way to 10.  After that, he said my number was 5.  I pulled out the paper with 6 written down, and from that point on, kind of thought the guy was a not competent.  I told that to the tournament director, and he got irate - but I later found reason to believe that they are friends.

He also did not tell me that he would be going through the set of questions three times, which made me nervous during the second set of questions, because I thought I must have screwed up something.

Is there any action that I should take against the administrator of the exam?  I'm already in the process of starting legal action against the tournament.  I offered to try to resolve this after I gave him the polygraph results that I completed, but he is refusing.

It's already tainted my view of fishing...

It's hard to let something go when you know you are right, and people are labeling you as a cheater. Also, this has the potential to prevent both my son and I from entering another fishing tournament.

Fisherman67 wrote on Dec 13^th, 2015 at 11:05pm:

Missing the correct number is not necessarily a measure of incompetence; at least the guy did an honest acquaintance test. 

Polygraphing fishing contestants is nothing new.  It's been part of the contests for at least 30 years that I know of.  Some of these contests pay thousands of dollars in prize money.  Contestants have been known to bring their own "catch", stuff a fish with lead weights to increase the poundage of their catch, etc.