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.