Yeah it was my first polygraph so I was sweating buckets! The polygraph was relatively simple though, they tell you all the questions they will be asking beforehand, so nothing unexpected is thrown at you.
I think I passed the poly cause if I didn't then they would tell me that instead of saying they selected another candidate and honestly I was so depressed and defeated that I just didn't bother communicating with them after that, 3 weeks of constant waiting and reaching out for updates and then finally getting an 'Unfortunately' email kind of did it for me.
Are you willing to name the company? Shame them here. This sounds wrong.
I do not know what the details of the situation were, for example was the offer contingent on additional background checks that you failed or on something else, but if it was related to a US security clearance I would seriously consider filing a request for information -- they are required to tell you their findings.
It would probably be an interesting reading (unless one has a very thin skin) and I would do it just for fun, regardless of the pulled offer. My 2c.