They're not legally liable for squat that happens to you when using their track.
"In order to win a premises liability case against the owner of a stadium or sports facility, you must be able to prove that the stadium owner was negligent (i.e., that the owner did something wrong).
Simply because you slipped and fell does not mean that the owner was negligent. Further, simply because the floor was slippery does not mean that the owner was negligent. The floor had to have been unreasonably slippery. Then, in order to prove that the stadium owner was negligent, you must prove that the owner knew or should reasonably have known that the floor was unreasonably slippery, and failed to take steps to fix the problem."
So, while it is absolutely correct that legal liability and vandalism (as well as control) are the reasons that they lock up the track (not school shootings! What a dumb thing to claim! There's no one at a track anyway) and that they won't say yes if you ask administration for formal permission, you couldn't possibly win a case against them and probably no one has ever done so unless, say, they knew that there was a sinkhole developing around the track that was about to swallow it up into the earth and did nothing to warn anyone. They'd actually make money from opening up the tracks, because then their students and friends of the university would be healthier and live longer and donate more to the college (or high school fund).