Ok I watched it again, and my opinion does not change much. I was wrong for saying it was Jarvis Green, excuse me it was Pierre Woods.
Woods had it though! You see him fall on the ball, and he has it. As soon as he got it, the ref should have blown the whistle, instead of allowing 8 guys to pile on top of Woods. The refs should have never let that become a pile. They just didn't see it I guess, and that allowed Bradshaw time to rip it away.
Who knows what went on in that pile. There could have been somebody on the Giants biting him Woods, or punching him in the groin area. Crazy stuff happens under there.
As far as Woods saying he never had possession, I think that is just him being embarrassed. I wouldn't want to admit to having the ball ripped away from me by a little scat back.
That's funny, I've yet to see a single angle showing the ball in Woods' possession. Yes he jumped on it, but that doesn't mean he possessed it.

There is no shot or angle that showed any Patriot was in possession of that ball following the fumble, and as anyone who was watched football for any length of time knows, once a fumble results in a big pile, it doesn't matter who had the ball first; it matters who has it last.
In real time, I thought Woods had possession. The way he fell on the ball, it was likely that he would have. However, one angle in slo-mo showed that Woods fell on the ball, but is right arm is trapped and he never gets a hand on the ball, but rather is laying on it, and you can see Bradshaw's hand reach under and wrap on the ball. After that, the pile-up goes on and Bradshaw, with leverage and a hand on the ball, was able to secure it.
Looked like the right call to me.