To point 2, there are scam calls in Asia that would show up as your child's phone number, with someone saying they're from the hospital, the child has been in an accident, they're going to operate but they need payment first. I guess even in the "bad parts" of the world doctors would never delay treatment due to money, but maybe some parents don't consider this in their panic.
I wonder if having a duress as well as normal password (like in https://www.youtube.com/watch?v=fx77j1vl4d8) is useful, but obviously if the caller is pretending the person is incapacitated, that goes out the window.
You are very lucky to live in a country where you can't even imagine that's an option. In countries like India, Pakistan, Bangladesh, ... doctors won't see you if you can't pay. In some places you even have to provide donor blood to be able to get an operation! Leading to nightmares like this:
I wonder if having a duress as well as normal password (like in https://www.youtube.com/watch?v=fx77j1vl4d8) is useful, but obviously if the caller is pretending the person is incapacitated, that goes out the window.