While I cannot point to any LAW, I believe that it has been VA policy for quite some time. Again, I can't point to any regulation, I've never researched it, but I do have a bit of personal experience, sort of second hand.
In 2002, a co-worker approached me, because I was known to be a firearms enthusiast. Her husband was seeking VA assistance, for both medical and mental issues. (technically this if hearsay, but I fully believe it) She told me that the VA told them, that they had to get rid of any guns, swords, bows* arrows, or anything like that, or they would be denied assistance.
He had an old Mauser 8mm and a Mossberg shotgun, and she came to me asking for help in selling them. I bought the 8mm, a nice VZ 24, and gave him 25% over current market value for it, to help them out a little. Also helped find a new home for the shotgun, as I personally didn't want it.
Now, what I believe is that it was VA policy for those seeking help with mental problems (and this was years before the current PTSD push) to have them remove "dangerous" weapons and items from their home. I believe they were "asked" to do so (the carrot), but if they didn't comply, they would be denied aid (the stick).
I find it extremely likely (particularly with the aid of anti-gun individuals inside the system) that this policy has grown over the years, and is now being applied in a more or less blanket fashion, as often as they can get away with it.
With recent administrations indicating that (at least some of the people in the administrations) feel that ALL veterans are at risk of PTSD, (the current buzzword) or even being closet terrorists, support from on high for the VA policy ensures it is not going to be changed, other than to expand it, at any and every opportunity.