Right, and the reason "everyone" has confidence in just waiting a bit for it to go back up without panicking and having to try to find an alternative is precisely because GitHub and AWS have on-call engineers that are alerted and immediately work on fixing it.
Of course, when a hospital’s IT systems go down, people do indeed have to endure it, but life does not always in fact go on [0]. Horses for courses, I guess.
Hospital IT systems failures are are mostly going to cause problems with scheduling, record-keeping, and billing.
By far, the most likely thing to kill you in a hospital is not the IT system but errors by the doctors and nurses. Or that you're too sick to save no matter what they do.