Well, not really. I mean, if you want to vote for Jericho, go nuts. I'm not going to stop you. But, you know, that's pretty poor justification. Is Jericho capable of the physical act of picking Cena up and hitting the Attitude Adjustment or applying the STFU on him? Sure. He was also physically capable of fulfilling the criteria for beating Cena in all their matches together, and he only did so once. In 2002, when Cena was a rookie. And, even then, just barely.
These two men had different primes in their careers, the prime of Jericho's Career never really crossed paths with the prime of Cena's career. Jericho went over Rock/Austin in his prime, not only did he go over them, but he went over them using their own signature finishing moves, wich just so happens to be the stipulation for this match.
2002 is also closer to Jericho's prime, which is why he went over Cena, close match or not. Cena's first match with Angle was a "Close" match, every match Cena has been in since joining the E has been a close match. He's been built that was since the beginning of his run, but he still loses, and even more so in gimmick matches.
Most, if not all the losses Jericho suffered to Cena, if not all of them where after Jericho's prime. Take both these men during the prime of there careers and there's no reason to think Jericho wouldn't walk out as the winner.
If we based this strictly on previous 1 on 1 matches, then we would all be voting AJ Styles over Kurt Angle, and Brock Lesnar would probably win every year. That's why I choose to look beyond the basic "match-up history" to avoid being pigeon holed into a simplistic thought or answer.
What's stopping Jericho winning this match isn't the fact that he couldn't fulfill the criteria necessary to, it's that he's plainly not as good as John Cena.
Arguably, in certain aspects. Wrestling ability, though, goes to Jericho, in ring work and promos go to Jericho, recent booking however goes to Cena. I wouldn't say Cena is better than Jericho, Cena has been booked better than Jericho in recent years, but those reason are more than obvious. Cena is the current face of the company, he's gone over everyone in recent history, so you can always use his track record to your advantage, but that doesn't change the fact that Cena still loses, on a somewhat regular basis.
I take it this isn't the track record of all those matches he's lost to John Cena, even when he's had the odds stacked overwhelmingly in his favour. Because if you brought up that proven track record, that'd kind of completely undermine your argument. So, yeah, don't do that.
Those matchup's all happened after Jericho's prime, prime on prime it's a different story, Jericho at his best was going over names bigger than Cena.
Instead you mention how Jericho beat Austin and Rock with their own finishers, which may be somewhat valid - albeit not as valid as all those losses he has against Cena - if it weren't for the absolutely crazy overbooked, dirtier-than-an-unwashed-car-in-June manner in which he gained those victories.
I'm not arguing that he won those matches in clean fashion, obviously not. I am however showing you that Jericho has been booked to go over the best, by best I mean "Better than Cena". The match stipulations clearly state that a manager can be present at ringside, that gives Jericho an advantage over Cena, especially if it's a McMahon in his corner.
John Cena wins this one. It's the only sensible choice.
I'm not saying Jericho picks up the clean victory; but the stipulation goes hand in hand with Jericho's most famous victories. Manager, check. Opponents finisher, check. Big name superstar in tournament style setting, Check. In Jericho's prime, with this stipulation, he goes over Cena.