You've got it. The idea is where is Currie is he walks away. BATNA is essentially what happens if both parties walk away, what position are you in?
It gets far more complicated with multiple parties and numerous deal possibilities. For example, let's hypothetically say that Currie DOES have a deal with Mike Bobo. If he walked away from the Gruden deal, he'd still have the Bobo deal (his BATNA).
Now, if the coalition of boosters have said, "If you don't accept the Gruden deal we've brought you, we will discontinue donations in the amount of [$ HUGE], then Currie's BATNA would be (Bobo deal value - Booster money).
This is essentially the game theory approach MIT talked about. The deal that is being taken to the University is good enough that they shouldn't say no, in addition, the penalty for failing to accept the good offer is good enough that they shouldn't say no. Hence, I believe, is why he feels so confident.