Jordan was JORDAN well before his fourth le. And where do you place Horry on the list then? Kerr? Are they among the Elite? I'm not trying to argue, but there are too many factors to say that number of rings is indicates a players standing on the all time list, although I can not that I argue with the first two on your list.
Number of les certainly isn't the only factor -- Horry and Kerr aren't there for the same reason that all the players on the 60's Celtics teams aren't. But when you're differentiating between all-timers, being the best player on a number of le teams is a pretty compelling factor.

You've also got Bill Russell, with 11 freakin' les, and Magic Johnson, with 5. You've got Shaq, Olajuwon, Chamberlain, Bird, Oscar Robertson, Dr. J. There are a ton of great players in the history of the league.

Timmy didn't change the league the way that Wilt, or Magic, or Jordan did. To crack the Top 5, much less the Top 3, he needs things that really set him apart from all the other great players. An obscene number of les would be one way to do that, and it seems more likely than, say, breaking Kareem's scoring record.