Fooly Cooly is my favorite creative expression ever produced by mankind. So, yes, I am a fan! I think I have a similar storytelling style as Fooly Cooly -- completely incomprehensible at first, but the clues are all there if you pay enough attention.
One of the three options with Doctor Madison is asking about the name of the hospital. Here's what she says if you pick that option:
* * *
"Oh, yes, that," Dr. Madison replies, as Faith wanders off to get a drink.
"Well, it turns out that if you donate enough money to a children's hospital, you can get it named pretty much anything you want. Some anime fan thought it would be funny. But I've never understood why some people think that just referencing something counts as a joke. Like, yeah, we get it, you can take the name of some obscure little thing and reference it in a different context. Some people will get it and some won't, but it's really not witty at all."
* * *
So, the longer story here is that I originally put that hospital name in as a placeholder, and my wife rolled her eyes at how dumb this was. The game is full of dumb little references. I thought about taking them out, but I thought it might be kind of meta to instead just have Doctor Madison poke a little fun at my lazy humor style.