The VA submits names to the FBI, to be placed on the list of prohibited persons, without either an adjudication or a commitment. That's beyond what the law calls for ... and that's the problem.
Do we know that is true? Personally, I doubt it.
As for VA care, I receive my health care from the VA and could not hope to find more personalized care anywhere. The caregivers up and down the line are focused on doing the best possible for the veteran/patient. I have private insurance but choose the VA care because it is far superior to anything I could find privately. The only downside is listening to other veterans complaining about everything under the sun.