It would be one thing if the comparison were fluctuating every year, or if they were close to similar teams. Because there is a lot of chance to it, but yes, circumstances of the team have effects. Jay Cutler fumbles more than Peyton Manning because of a ton of factors, including OL quality and the QB's ability to get rid of the ball. But to have one team so far outperform other similarly situated teams is shocking.
That's just the thing though. There ONLY outperforming teams if you:
A) Remove dome teams, which is suspect at best. Here are the numbers I have from 2001.
Domed/Retractable: 111 seasons worth of games, 2,507 fumbles, average 22.59, SD 6.63
Outdoor: 336 seasons worth of games, 7,397 fumbles, average 23.62, SD 6.03
The 3 fewest fumbling teams are Indy, Atlanta, New England.
Indy has 90 fumbles over the past 4 seasons, which is an average of 22.50. Andrew Luck has 29 in 3 years. Their 14 year average is 18.5 fumbles, and their average from 2001 to 2010 was 16.9 fumbles/season. Indy is in the position they are in because Peyton didn't fumble all that much. 43 times in the 10 years he played before his neck injury. Whatever benefit there is to playing in a dome, it coincidentally didn't stay with Indy after losing one of the greatest QBs to ever play.
Atlanta has the same number of fumbles New England does since 2007 at 121. Prior to 2007 they weren't particularly great. Why? Cause Vick and all the other guys they trotted out there were fumbling an average of 12.3 times per season. In 2008 they drafted Matt Ryan and he's only fumbled 33 total times since. Average for Atlanta since 2007 of 5.1 fumbles per year. Whatever benefit there is to playing in a dome it, it coincidentally didn't help Atlanta do anything grand before they drafted a franchise QB who's very good at protecting the ball.
B) Completely ignore that QBs account for a large portion of a team's fumbles, and come varying abilities.
San Diego plays outdoors and they have fumbled 147 times since 2007 compared to New England's 121. Rivers has fumbled 67 times in that span while Brady/Cassel have only fumbled 44. Excluding QBs, San Diego has fumbled 80 times and the Patriots have fumbled 77.
Since Joe Flacco was drafted in 2008, the Ravens have fumbled 138 times and the Patriots have fumbled 104 times. Flacco has 62 fumbles, and Brady/Cassel have 37. Excluding QBs, the Ravens have fumbled 76 times and the Patriots have fumbled 70
Packers have 159 fumbles since 2007, 70 of them from QBs. Excluding QBs 89 fumbles since 2007 to the Patriots 77.
IMO, it's pretty damn clear to see that QB's play a large part in the total number of fumbles a team will have. I looked at the top 20 fumblers from each season since 2001 and there has never been more than 2 non-QBs on the list in any year.
Teams fumble at wildly different rates because QB play quality is wildly different. QB play is also predominantly shitty, and the majority of the league plays outdoors. It just so happens to be that Indy and Atlanta have - or have had - very good QBs while playing indoors. That's no reason to exclude indoor teams, not when it's pretty apparent that the benefit in fumble reductions that they have seen for these two teams at varying points have been almost largely QB driven.
There is no other team in the NFL that can say they have had a QB as good as Tom Brady at both ends of the period of observation. Shit, there's only a couple that they can they have had a QB as good as Brady the entire time since the rule was put in place.
Excluding all QB fumbles from 2001, the Patriots have 166 fumbles. The Chargers have 159 fumbles, Kansas City has 167 fumbles, and Atlanta has 157 fumbles.
Jacksonville is 8th overall in fumbles over the 14 year span with 304 fumbles. The Eagles are 21st with 346 fumbles. After adjusting for QB fumbles, both teams have the exact same 181 fumbles.
Edit:
Figured I'd throw in another stat I looked up. Passes dropped since 2001. Patriots are ranked like 5th or 6th in highest percentage of passes dropped. Indy and Detroit are also in that area, two indoor teams.