Okay from everything I am reading (and really great thought mist)
Right now I too get the feeling from the stuff posted that somehow, someway the lie, twist, regret are all interwined in some fashion as mentioned

THE LIE:
Jon is the liar and we also know Jeff can't stand him so needless to say, combining that with the information we have on Jon, this is probably a lie that pretty much envelops his character as it is. We also know that it is a flat out lie, not an embellishment but something he completely lied about, fine.

One question I have is according to Jeff, he did not know about this lie at first - so it must have been something that screening their background didn't show b/c Jeff states he didn't know it was lie and then when he found out he claimed his MF expletive. So it wasn't something that he could have easily seen was contradictory to Jon's screening or he would have known it was a lie at the moment Jon spoke it (this is obviously spec) Now the OTHERS according to Jeff don't know either or he doesn't believe they do, hence his comment about them finding out watching with us.

THE REGRET
How does one feel regret if no one knows about what the person is regretting? Does he feel regret solely because he ended up screwing himself out of the game? I can see that considering what "type" Jon appears to be OR he has regret which is shown in a confessional that the other contestants don't know about but by that time, Jeff does.

The bottom line for me is that while I do believe this may have been ballooned out by Jeff, etc. I do feel this lie had to be significant enough (and I think we can come up with little lies that don't deserve this embellishment) for this huge propaganda put forth.

THE TWIST
How this relates to the twist. Like misto said, could this lie have managed to get someone out of the game, i.e. Trish? The problem is Trish coming back and calling him out on it means then they learned the lie and according to Jeff, he doesn't think they know.

I even thought b/c of the lie, he ends up getting ejected from the game which is why they have the twist to replace him as a player but then wouldn't, again, the contestants know - unless they were not told WHY he was ejected?

My biggest issue is I can't see how they wouldn't know about the lie until viewing it on television