If you own a car, you have an alarm on that car, you put The Club on that car, you lock that car, you keep that car in a locked garage, and you keep those keys on your person at all times; you know, every reasonable security measure; and that car is stolen and used in a crime or involved in an accident, you are not liable. In fact, you can to much less to secure that car (pretty much anything that doesn't involve leaving the keys in it or handing the keys over to someone else) and still not be held liable for the actions of another party who used your vehicle.
This is very similar to an internet connection, in that it can be secured or not secured, used with permission and used without permission, even used with or without your knowledge, and the rules of liability should be similar, as well.
To blow another large hole in your gun analogy, I'd like to point out that, in most jurisdiction within the US, if it can not be proven that you fired the gun, it must be proven that you willingly supplied the gun to whoever did fire it before you will be held liable for the results of that firing. [primary source: my father in law, credentials withheld due to active duty status (nonmilitary); secondary source: my coworker's stepfather, a recently retired cop; tertiary source: my coworker's mother, a recently retired police dispatcher] Even your analogy indicated that the "owner" of an internet connection should not be held liable for the use of that connection to commit an infringement unless, as is the case with a car or gun, it can be proven that they, or a party they explicitly authorized, were, in fact, the one who used that connection to commit said infringement. The laws governing liability for acts committed with firearms and vehicles do account for security, as well, in that they do place liability on the shoulders of the owner if a vehicle is left with the keys in the ignition or a gun is left sitting out in the open, or similar situations where parties not explicitly authorized by the owner may have easy access; the law places liability on the owner in those cases, and I agree that similar laws regarding internet connections should place liability on the "owner" of the connection when an ethernet port is left in an unsecured location (e.g. unlocked utility box on the side of the building) or a wireless router is left unsecured. The flip side of that is that, if steps are taken to secure the resource, just as with firearms and vehicles, liability should fall on the party who circumvented those measures and used the resource without the permission or knowledge of the "owner".
The law is already very clear on this, but for some reason people get confused when you throw in the phrase "on a computer". See: USPTO.