The problem from the university's perspective is that while $13M is a low-ish amount of money (by university standards), the university has no reason to believe it would "put the problem to bed." If the university backs down, the strikers will be able to dictate any terms they want in the future, and any such strikes (i.e. illegal ones) would certainly have many more participants. The disruption to university operations could be severe.
And this is why unions exist in the first place and make binding contracts - no one wants to make a deal with another party when the other will arbitrarily decide the deal isn't good anymore and act like fools contrary to the terms of the contract.
And this is why unions exist in the first place and make binding contracts - no one wants to make a deal with another party when the other will arbitrarily decide the deal isn't good anymore and act like fools contrary to the terms of the contract.