The "with Patriots/on other team" article is disingenuous since they use totals rather than analyzing the distributuon. Welker and BJGE pretty much sway the entire thing because of the others who have a meaningful sample on both sides - Morris, Woodhead, Blount, Moss and Taylor - two are virtually identical, one slants mildly in NE's direction, one slants mildly in the opponent direction and only one actually tilts in NE's direction. The players who don't have fumbles with NE, and thus no fumble rate, could easily be small sample anomalies. Of the remaining players - Watson, Amendola, Jordan, LaFell, Tate and Maroney - two have far too little touches on one side to mean anything (one in each direction), one is basically even, two tilt substantially in the opponent direction and one leans toward NE.
It is a classic random distribution with two outliers.
Even more noteworthy, though, according to ESPN, Welker had zero fumbles for Miami or Denver, either as a receiver or a runner. It is possible that he fumbled the ball 13 times in those four seasons on special teams, but not very likely.
http://espn.go.com/nfl/player/stats/_/id/5941/wes-welker
So, the distribution appears to be purely random, and one of the guys that the average rate depends on appears to be wrong. You don't have to be wearing a hoodie to find this analysis unconvincing.