The 2013 Heat were 23rd in total rebound%, obv well below average.
https://www.teamrankings.com/nba/stat/total-rebounding-percentage?date=2013-06-20
For comparison: 2015 Warriors 16th, 2014 Spurs 15th, 2012 Heat 12th. No correlation at all for the last 6 years. Teamrankings doesn't go back past 2011 though, and I know the 2009-2010 Lakers were huge on rebounding (especially offensive) like this year's Thunder.
I don't know how tight your definitions of "inside offensive presence" and "inside defensive presence" are. I'm not sure Bosh counts as either; he did much of his damage as a small-ball 5 that could space the floor and guard the perimeter on switches. It's hard to imagine a team that has a complete zero for both of those. Shaq, Duncan, Pau surely count and that covers nearly all the rings since 1999.
I can't even agree with "best chance" though. The Grizzlies formula mostly failing in the playoffs plus the Warriors winning the le last year makes me lean away from such absolutes. A damn good team is a damn good team, regardless of if they prioritize defense, rebounding, shooting, or whatever.
I'll admit that "revisionist history" was the wrong term for me to use. But it seems that you're just proclaiming that the strength of the best team of the moment (OC) is what the entire league (or even just the Spurs) needs to do. Would you change your mind if the Warriors come back and win the series? Especially if it's playing their own way? Or if the Thunder lose in the Finals?