It's pretty obvious that Marner and Matthews both had significant issues with Babcock. So let's rephrase the question a bit here. In any workplace, is it likely that someone would want to be paid more to stick around if they had to put up with a boss they can't stand? Even if they want to stay for other reasons?
To me that's an obvious yes. As such, it's equally obvious that it likely played some role in the negotiations. It's a cop out to assign all the blame to Babcock though.
Regardless, I'll reiterate what I've said a hundred times already. We need to stop obsessing about these contracts. There's no difference between the overpayment of our RFA contracts and teams spending $2M too much on their marginal players, which a large part of the league does. It's the amount of overpayment that matters. That people seriously argue that our chance to compete is over because of that is beyond me, when some other contenders carry contracts with twice as big of an overpayment for a much less important player.