So what you are saying is that DX, Evolution,the Corporation, the McMahon-Helmsley Era, and The Two Man Power Trip are not defining moments? Ok so you want defining matches. Well here's a couple:
1) Hell in a Cell vs Jericho : What makes this match memorable is not the fact that HHH pinned Y2J on top of the cage but ever since no other Hell in a Cell match as seen action of any kind on the top of the cage.
2) Hell in Cell vs Foley At the time, this was Foley's retirement match.
3) 2001 Quad Injury This happened during a tag match of HHH/Austin vs Y2J/Bennoit. HHH should of quit the match right there but instead he kept going, letting Jericho put him in the "Walls" to finish the match.
These and everything I said earlier is why HHH is great. Remember too, if it wasn't for HHH there would be no Sable. Also when Hall and Nash left for WCW, HHH was the one who got punished for "The MSG Incident" but he took it like a man and didn't complain and cuz of that punishment SCSA won the King of the Ring.
I can appreciate the fact that you actually provided great points to your argument, so let me clarify my position a bit. Triple H is undoubtedly one of the greatest we have ever seen. I never bought into the argument that he doesn't deserve all of the accolades he has achieved because of his marriage to the "Boss' Daughter".
But when I bring up the defining moment, it is something that is hard to explain, but most fans will know what you are talking about. A defining moment is not only a moment that you can use to say "This was the best thing that he did in his career" but it is also something that at that time was the biggest and most successful match or program in the industry at that time. I think a wrestler's "defining moment" doesn't only act as a reflection of his career, but also as a reflection of that time period.
When DX was at its hottest and Triple H was at the helm as its leader, the industry was absorbed with McMahon vs Austin. When Triple H was in the Corporation, it was still about McMahon vs Austin and later Rock vs Austin. Triple H did get the spotlight during the McMahon/Helmsley era but in my personal opinion, that entire program just didn't get over as much some of the previous years feuds. I'd be interested to hear some other opinions about the McMahon/Helmsley era in 2000. The Two Man power trip would have been HUGE and had a HUGE payoff had Triple H not gotten injured.
I think your strongest argument is with Evolution, as they were one of the best executed stables in many many years. But in the entire time Triple H was in Evolution, can you think any feud he had that you can honestly say "Wow, that was one of the best things I've seen in years"? His feud with HBK and the break up angles with Orton and Batista are the only things that stand out in my mind, and of those feuds, the only great matches I can think of is the Triple Threat from WM 20 and the Hell in a Cell with Batista.
You brought up the Mick Foley Hell in a Cell match, and while agree, it was a great match, that match does not stand out compared to the rest of either Foley's or Triple H's catalog of matches.
Again, I am not bashing Triple H. I am a HUGE fan, as I said, I think he has one of the most believable gimmicks in the industry. But I stand by my statement, when compared to the other cornerstones of the WWE, the one thing that Triple H lacks is THE match that everyone will talk about 10 years from now.
For HBK, everyone will talk about the ladder match or his match with Taker. For Ric Flair, it's his match with Steamboat or his Wrestlemania match with HBK. For Austin, his WM matches with The Rock or his feud with McMahon. Foley, his first HiaC. For Taker, his match with HBK and his first and second HiaC. Hogan, his match with Andre. Savage, his match with Steamboat at WM. I honestly don't think Triple H has a match that he can put against these classics.