Like TennJed said, if a patient complains about depression he/she should expect those questions from any doctor, VA or not. That is why I am always careful what I say around medical providers. Even if the questions are not asked, who knows what they write in their notes.
Having said that, I was at the VA just this past Friday and there were no questions about firearms. I have always been satisfied with the treatment I have received from any VA clinic/hospital I have been to.