I don’t think so. Stanford has several suicides a year. Any theoretical liability from and outdoor accident is a rounding error on their total liability for student deaths, morbid though it is.
The consequences to the university of being labeled a white supremacist institution would be far greater than a few student deaths per year. Stanford’s reputation would never recover, if that label adhered. The university would shrink to nothing and vanish. Not one whiff of a hint of liability to being labeled racist in favor of white people can be tolerated. If that means a total ban on supporting outdoorsmanship, so be it. The university survives.
For that reason, fighting white supremacy is the keys to the kingdom for despot administrators, and the definition of white supremacy is undergoing an accelerating expansion that will soon extend past the edges of the universe.