no, that's not it. I do play in the infinity tournament, but my rank there is unrelated.
I just realized that what I called "ranking position" is actually called "rating position"... sorry if that caused confusion. What I'm talking about is the messages you receive when the game ends. It says stuff like
old rating: 2145
newrating: 2172
rating position: 15th
My guess is that either two or three of your three rating position lists are omitting inactive players, but that either (1) they use different standards for what counts as an inactive player, or (2) they update their inactive player lists on different schedules.