In practice, if you change surgeries or one ceases to exist, your medical records should be transferred to your new doctors. So they can then answer the relevant question, that being have you ever been diagnosed with any of these conditions or anything else that could affect your ability to be safe. In any case, it'll more than likely be an office worker who checks your record and leaves it on the doctor's desk to sign.
These days, you most likely will go decades without seeing a doctor. Most conditions are dealt with effectively by nurses or nurse prescribers and even if you get an appointment with a doctor, it'll likely be a 'phone consultation. And for all they know, you could be marching up and down your living room dressed as Napoleon.
It's simply a questionnaire for them to fill in. They aren't certifying you as safe to have guns. Merely stating there's nothing in your records to give rise to concern. Which is why the doctor saying "I'm no expert on mental health issues" is really just copping out, using a bad reason not to do it.
