No, they certainly don't need that information.
So I presume you also don't believe they need to know if you have a motorcycle, a meth lab, or a Presa Canario breeding kennel. All of these have a high correlation with accidental death of self and children in the household--or permanent injury. It's your doctor's duty to maximize your life expectancy and minimize your likelihood of permanent injury. In order to do that he needs to counsel you on the best ways to avoid killing or maiming yourself in pursuit of your hobbies. He can't do that if he doesn't even know what they are.
Of course this all comes down to trust, and if you don't trust your doctor you should dump him and find a more trustworthy one.
If they are concerned that I'm suicidal then they have to presume that I might lie about having a gun anyway and that even if I don't currently own a gun there is nothing to prevent me from buying a gun and ammo on the way home, so the fact of my owning a gun at that particular time is not at all relevant to any medical treatment they would give me.
Suicide is only one way people die from bullet wounds. Accidents happen through negligence, drunkenness, lack of training, and letting a gun (or other instrument of death or permanent injury) fall into the wrong hands, such as those of a child. There's also the phenomenon of an armed person feeling cocky and mouthing off to someone who is quicker on the draw, walking into a neighborhood where he's likely to encounter one of those people even though he has no good reason to be there, or risking his life to avoid having fifty bucks cash and his credit cards stolen.
A straight-A student, football star, kindest kid in the neighborhood was recently killed in DC Southeast merely for
wanting a gun. He saved up the cash, walked over to the house where his lowbrow friends told him guns were sold, and the dealer sized him up and decided to simply kill him and take the money without having to give him a gun in return.
If you claim it is, then simply tell me what specifically they would do differently if I answered YES to that question vs NO and why it would be appropriate to presume "Not Today" is the same as "I'll never own a gun".
Why ask me? Surely you have a family physician who could give you a more accurate answer to that question. As I said earlier, he would probably ask about your training, the way you store the gun, under what conditions you take it out, where you go with it, etc. He probably already has a pretty good idea of whether you have any suicidal tendencies.
If he's a trained psychologist or counselor he would probably not need to ask the questions. He knows he'll get more accurate information by correlating information he gets from your conversations. It's hardly difficult to get someone with a gun to casually refer to it, and to the things he does and does not do with it.
Again, there is absoutly NO DIFFERENCE in how you would treat a patient based on their answer to the question, "Do you own a gun?" and thus it is not relevant to any medical treatment.
And as I have just detailed, you're dead wrong on that.
You claim there is, then tell me specifically how you would alter the treatment based on the answer to that question?
Doctors do more than "treat" patients. Assuming you're not one of those old reprobates who only consults his physician when he's on death's door. When you get your annual physical he asks you about all the medications and supplements you're taking, how much exercise you get, your eating and drinking habits, etc. Your avocations, habits, hobbies and living environment have as much bearing on your future health as your blood pressure, prostate size, colonoscopy and BMI.
Note, the answer to this has to come from a standard medical text indicating the different treatment based on the answer to this question.
You're pretending to be obtuse, which makes you look like a buffoon since scholars have much better ways of arguing. I'm sure you know better than this. This is not the Middle Ages and "treatment" is not your doctor's sole responsibility. "Prevention" is a major part of his job. Prevention of accidental death or homicide, or simply shooting off your toes, is included in that. Suicide is a straw man in this argument.