If it's any comfort, most people have push notifications turned off for the main Facebook app (understandably since we send quite a few of notifications). However anecdotally some of the survivors of the attacks mentioned that they got phone calls from concerned friends / families while hiding in the Bataclan, which was understandably stressful.
Maybe for this kind of events (when people need to hide) you should postpone the push until the situation become calmer?
On the other side, the push notification can alert people yet unaware of the situation, and save their life.
I guess we will have to wait until Facebook brilliant AI team can automagically figure when it's pertinent to push that crucial notification!
What kind of context hints could be used? heartbeat rate? analyzing ambient sounds like screams, detonations, explosions, or silence? analyzing surrounding voices to detect emotions like anger, distress, pain or fear in smartphone owner voice or other people? extracting dangerous location from media streams, and correlate with geolocalized users' positions? using other geolocalized users' answers (safe/not safe)?
I'm aware some proposition are not really realistic (yet) or somehow really creepy.
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Also, back to earthquakes, using context hints of lot of smartphones going from 'still' state to 'tilting' state, in a relatively localized region, could you detect earthquakes occurring quasi real-time? and push a warning notifications to your friends faster than the quake waves? « possible incoming quake in 5 seconds, brace yourself » ( à la https://xkcd.com/723/ )
In my opinion, "other things are just as bad" is as good an argument as "if you turn it off, it's not dangerous".
I still think it's not smart to send push notifications in an active shooter situation for a feature that is made to give people who are not involved peace of mind. If you consider such risks, and not get defensive right away, you will find that solutions can be pretty simple, e.g. a banner inside the app, instead of a notification.
I think shooting was aready over before people over at Facebook even knew something is going on. I imagine they wouldn't even turn it on before the information hit mainstream news.
Most of the trainings that I've gotten for active shooter-type events (gov't employee; they're frequent these days) advises you to silence your phone since the first thing that's gonna happen when the news shows up is everyone is gonna call you anyways.