Both of you are right, but it's not regression to the overall mean, it's regression to that team-season's mean. Turnovers are not predictive season to season, but within a season, I'm still going to argue it's a different case.
Yes, fumble recoveries tend to be 50/50 in the long run. But an individual team-season may have players and/or scheme that causes more fumbles, resulting in a larger quantity of net recoveries. Same with interceptions. Yes, the random errant pass can hit your DB in the numbers, but there'a baseline of that for everyone. But due to players and/or scheme, more INT opporutnities may come a team's way and thus - more net interceptions.
I guess what I'm saying is everything you said is right AND what I'm saying is right. I'm the king of deferring to the rules of statistics, and I don't believe I'm resisting them in what I'm saying.