I'm not so sure about that. I think every firearm has to be registered so they pretty much know who has what.
Only certain ones. In the 90s the Canadian government attempted to impose a national registry of all rifles...there was so much noncompliance, misinformation, spamming etc. that they finally had to give it up.
Not to mention lots of war trophies and “lunchbox specials” never got registered, and many small arms disappeared from Canadian Forces bases over the years.