What exactly does the bolded mean? What did you want BK to do in this situation? Say "Hey, I know you think he's got vertigo, but it could be something else...take him to the hospital?" What in his expertise, training, etc. equips him to make such a suggestion? Millions of people have the same symptoms that Brooks had, over a prolonged period of time, and have...vertigo. Not a brain tumor. This is some incredible Monday morning quarterbacking going on because we have the benefit of knowing that this is the one out of a million case where a person actually did have a serious problem, and it is really easy and lazy to point fingers.
Any decisions about diagnosis, treatment (even if they are just making suggestions, which is what you seem to be suggesting BK should have done), etc. of an injury or illness a coach should have absolutely nothing to do with. That has always been a big no no. When a guy gets a concussion or suspected concussion, for example, the coach has absolutely nothing to do with the protocol. It isn't up to him to decide if a player has a concussion or not, decide or suggest to the medical staff what the treatment should be, or when/if he should play. It is completely out of the hands of the coaches. This situation should be no different than that.
If I'm a head coach and a player comes down with some sort of non-football related illness, I'm sure as hell not suggesting any particular course of treatment. What qualifies me to do that?
If there's a case to be had here, it seems like is against LSU's training staff or the surgeon at the hospital.