In every jurisdiction I have ever worked in, “competence” is a matter of court-determined cognitive abilities, not a matter of sanity. Competence is also situation specific.
For instance, a person may be crazy as a loon, but if they are capable mentally do basic math, balance a check book, pay their bills, and shop and prepare their own food and such, they cannot be declared incompetent with regard to their monies, and a conservator to handle their finances cannot be appointed against their will, even if they choose to spend their money on drugs and alcohol, etc.
Similarly, an ill person with intact cognitive functions who cognitively understands their medical condition and the proposed treatments, yet chooses to forego recommended lifesaving treatments for any other reason - even voices telling them to do so, or such - cannot be declared incompetent to make those decisions, and cannot have a treatment guardian appointed to make such decisions against their will.
Competence is a cognitive determination, rendered after a specific, independent evaluation rendered by a psychiatrist or psychologist who has tested for the cognitive abilities pertinent to a specific situation or function. The ultimate determination is a legal opinion rendered by a court, and during this legal process the person being rendered incompetent may defend themselves, enlist attorneys, and ask for their own, or a court-appointed, independent evaluator. As far as I know, some person or agency cannot simply declare someone incompetent until they are able to prove themselves otherwise.
I doubt these VA letters were predicated on such legal processes. I doubt very many vets, except those with brain damage severe enough to render them unable to ever learn again how to safely fire a weapon, could meet the legal requirements I have always practiced under. Mere PTSD, or even suicidal or homicidal tendencies do not imply cognitive disabilities of the sort required for “incompetence” to handle a gun. Evidence, presented in a court, may convince the judge that, due to a mental illness, “immanent and substantial danger to self and others” exists, and that may lead the judge to adjudicate the person “mentally ill,” and THAT may preclude firearm ownership, but that is not the same issue as the legal term “competence” used here.
[May I remind you that the obligatory FR requirement to include professional and personal slurs and vehement loathing overall when replying to posts by a shrink is - as far as I know - still in effect. Please don’t skimp on the venom.]