Right, but if someone steals your registered gun and uses it in a crime that gets traced to your gun, the police will be visiting you, if not arresting and prosecuting. For this reason, I'd assume it's smart to do what you can to avoid having your gun being used by strangers. For the same reason, you could argue it's smart to not let strangers use your internet connection, even if theoretically you can make a case that you're not legally responsible.
This varies by country. In Australia if I want a gun I need to have a firearms license, I have to register every weapon I own and store them in an safe that meets certain minimum requirements (separate ammunition, requires key and combination to enter, minimum thickness, rules about how it is secured to the wall/floor, etc) and at any time the police can show up and ask me to show them I have the weapons correctly secured.
Or I could rent appropriate storage space at a gun club, store the weapons that way.
It's a completely different gun culture to what is seen in the US, and personally I like it a lot more.
You also need a valid reason to have a gun- you can be a member of a gun club and be a recreational shooter, or for animal control (my license) but to have that you have to have a property to shoot on
At least in the US, private sales are legal, and there is no requirement to file any paperwork whatsoever.
Moreover, there is a staggering number of firearms that predate any sort of government record-keeping. It's not like these are muskets and black-powder revolvers, either - most of the designs for hunting rifles and shotguns are nearly unchanged from models that were available a century ago.