Yeah, we don't know the whole story. It's not impossible that this is a situation involving both systemic flaws and someone who is just intractably and unapologetically incompetent -- for instance, someone who has habitually browsed non-work-related websites and been warned against doing so, but the harm of the distraction was never actually a danger until this fake alert incident.
For me, what partially redeems this employee's firing is that the head administrator was also terminated. If this "button-pusher" deserves to be punished for incompetence, then whoever thought it was OK to have such an incompetent person pushing the button also deserves to be punished.
For me, what partially redeems this employee's firing is that the head administrator was also terminated. If this "button-pusher" deserves to be punished for incompetence, then whoever thought it was OK to have such an incompetent person pushing the button also deserves to be punished.