"Without cause" is a legal term based on the conditions of her contract. If the school claimed they had "cause" to fire her, then the school would risk being taken to court to prove she had violated the specific terms of her contract. This conceivably could cost tons of money in court costs, etc. By firing her "without cause", they choose to just pay her off and be done with it.
Notice this is Oregon State University, not the University of Oregon. If it was the U of O, they'd probably just get Phil Knight to pay her off out of petty cash.
BTW - one of my grandsons who is 12 is a huge Beavers fan, but even he has said their womens basketball program "sucks".