I think that it's said that the phone automatically warns the emergency contact even if it's screen is broken.
It would means that Lucy was the one calling the hospital after getting the emergency notification.
Mind you, that comment was almost 2 years ago so those lines were possibly changed by now. At the time it was one of those things that stood out as "Wait a minute...", know what I mean? Unless you mean real life phones, that'd be a huge TIL for me
That being said, it has been a while since I last played, and I've been meaning to check things out to see how they've progressed since I last played. Appreciate you having me return to this one sooner than I would otherwise <3