"Patriots backs simply don't fumble": Yes, because if they have a fumbling problem, they stop playing until they fix it (Ridley) or they cease being Patriots if they can't fix it (Maroney). Belichick is well-known for having a "doghouse" for running backs who fumble.
"Your explanation isn't supported by the data": I wasn't trying to give an explanation supported by the data. I was trying to give an explanation for the data that makes sense and is supported by observing the Patriots play.
It's like saying Magnus Carlsen must cheat at chess, because the chance of him making so few errors is effectively zero assuming he makes errors at the rate that other grandmasters do.