I've never heard of this form or even this professional association, buta dealer can deny a sale to anyone for whatever reason. We have a legal duty to do so if we think it might be facilitating an illegal transfer (e.g. "straw purchase"), but it's been my experience that you can't go by appearances. We had a guy who looked like he was right off a prison bus who got cleared faster than I do for a purchase, and another time when a cop - in uniform and on his way to work, no less- was outright denied (supposedly a case of mistaken identity).
You may have a right to have guns, but nobody has a duty to sell you one.