I've no doubt there were serious concerns about her suitability, but this being a future where treatment for various physical and mental ailments has presumably advanced a great deal, it was taken as gospel that if she were able to nail the entrance requirements - including checks for just this kind of instability - she would make it in. History alone isn't enough to disqualify when that history presumably lead to (often effective!) treatment.
By comparison, someone born paraplegic in the UEF could doubtless get into the fighter corps assuming their paraplegia was no longer an issue at the time of application and they could pass the physical standards.