This isn't a question of knowing a service is down. We're assuming the team that is fixing the service, knows it is down. It was a question of not having the resources to direct literally any other person in the org to log into an admin panel and flip a toggle from green to red.
I was merely addressing the "thousands of employees" non sequitur. Org structure means that the raw number of employees is a meaningless metric. The only people who are going to potentially flip that switch are going to have some sort of direct responsibility for the product. That number is going to be very similar whether it's a large company like Amazon or a smaller one like, say, Heroku or Dreamhost.
The issue has nothing to do with a lack of manpower to flip the switch, whether it's 1000s or 5 people, is the point.
People responsible for the product should not have say over the switch being flipped, for obvious reasons (illustrated in other comments in this thread).