The idea of a child shooting a gun might not be as appalling as it at first appears. In gun owning cultures like parts of the U.S.A, it is generally considered desirable to start the kids shooting very early - in single figure years. The idea is to instil firearm safety instincts that the shooter will then automatically follow throughout their lives, and find psychologically hard to forget or to break.
In the case of American kids who ‘own’ rifles like the Ruger 10-22, I would think that the majority of them only get to ‘have’ the rifle under parental supervision. In other words, they only hold or clean or shoot the gun when the parent is there. Otherwise the parent has it locked away in his or her gun cupboard/safe. Sort of like what @Skide suggested, actually.
Well that’s what it should be, anyway! No doubt some assholes have thought it perfectly OK for their kids to have the gun under his or her bed.
(Indcidentally, .22LR is not considered powerful enough for human-sized animals, or even for bunnies that are more than 100 yards away. This might contribute to the reason why more U.S. civilians are killed by it than any other round - people underestimate it.)