I think that the only people who would know the answer to that question aren't talking (and will never talk) and that those who claim to know the answer don't know what they're talking about.
Seriously, who would know? I can only think of three parties.
Brady: "Yeah. It was me. I made them trade Jimmy." Not happening.
The Krafts: "Yeah, we're richer than God but one of our employees made us force Belichick to trade Jimmy." Huh?
Belichick: "I don't really have control of the Roster and so I couldn't stop Tommy from making Bob force me to trade Jimmy." Nope.
I'm not saying it didn't happen or that it couldn't have happened. I'm just saying we'll never know...unless his publisher adds an extra Zero to what will already be Belichick's seven figure Advance for his Memoir, but I'm not holding my breath on that.