The flaw in the Remington safety was a failure of the sear to reset. That is the condition where the weapon (it doesn't have to be a rifle) is cocked with the safety on and the trigger is pulled. If the sear fails to reset after the trigger is released, moving the safety to the Fire position will allow the firing pin to move and the rifle to discharge.
This is due most often to work on the sear or cocking piece in an attempt to lighten the trigger pull. In the Remingtons, it was due to a slight shifting of the trigger block plus incorrect modification of the trigger pull. IMHO, the main cause of at least one death was failure of the gun owner to keep his rifle pointed away from a fellow human being. The idiot was playing with a loaded rifle in the back seat of a car and it went off and killed the man in the front seat.
BTW, failure to reset can occur with all bolt action rifles (including the Winchester 70) if attempted adjustments are made improperly.
Jim