Is it an infringement of Privacy Rights?

Is it an infringement of Privacy Rights? I ask this because while researching the subject of my videos on youtube http://www.youtube.com/watch?v=MA54KVNqFvA
http://www.youtube.com/watch?v=X3tIPW4GlcM I discovered many spree killers just didn't drop from the sky.
In fact they were either diagnosed or treated for certain mental health problems. I would suggest that perhaps many tragedies could have been avoided by placing a note in a file that could be accessed by authorities. While I am ardent in my belief that there ought to be an unfettered right to own arms by law abiding citizens where does one draw a line? Would it be an invasion of privacy to have such information in a data base? I am not opposed to background checks where an individual is proved to be indeed law abiding before they purchase arms. Why not "Mentally fit"? say for instance they have a diagnosed personality disorder and a note comes up when their backgrounds are checked and the shop keep says no sale. Would it not also be fair for them to get a certificate from their doctor saying yae or nae. Of course I can see the room for abuse of this by certain people who have an agenda like the social re-engineering of society basically saying no one is mentally fit to own arms. I can also see that some people would just not see a mental health professional for their troubles for fear of being labelled. Sadly the governments of the past and present have used a simple solution to very complex problems.. "The Firearms Act" which has made it a criminal act to possess a firearm without a licence. There problem solved. right? Indeed, If this were true then Kimveer Gill would have not been able to obtain a firearm to carry out his crimes. He was also known by the mental health professionals yet no one seen fit to even say "Hey watch this guy". No instead the agenda is disarm everyone it's safer.