My guess is that those two were among the first cases of humans who possess the ability to see fairies, and at the time the complete lack of evidence of the fairies' existence caused such cases to be misidentified as mentally ill, thus why both of them were in the hospital and Tokonatus is so terrified of the fairy (he thinks he's hallucinating and is fed up with being unable to do anything about it as well as how it may have ruined his life at the time).
I was going to post that speculation before, but I thought this page made that unlikely. I mean's there no way freaking Fubuki would have been thrown in a psychiatric ward... right?
Ehhhh, some hospitals make you put on gowns for doing the bog-standard health check (because of the ECG and chest X-ray and whatnot - and the X-ray is usually in radiology (or an X-ray truck), not the check-up center). It could just be them at the hospital getting the mandatory testing.