If you have followed my writeup of "The Devotion of Suspect X", you may have noticed the main characters are all graduates of Teito University (帝都大学). While the "Galileo" mystery series may be the most visible example today, Teito university is the home of a number of fictional graduates or the setting for fictional events.
So it is entirely appropriate that Teito university itself is nonexistent. It's one of those things, like Acme Corporation in English, that exist only by the implicit consensus of the writers using it in their own fiction. Another Japanese example is Maichō Shinbun, a fictional newspaper frequently used in television series and literature. The Necronomicon is a fictional book originally made up by Lovecraft that appears in many works of horror or fantasy fiction.
The appeal for writers is that the reader or viewer is likely to have vaguely heard of it already. We are hardwired to see familiarity as a proxy for importance and plausibility (this is why "branding" advertisements work) so the writer gains a sense of veracity with little effort. You can get the same effect by using real places and placing real people in fictional stories of course. But there's no basis in reality, so the writer is free to add or change whatever features they wish. If a writer needs Teito university to have a particle accelerator or Maichō Shinbun to have a Paris news bureau, then they can without anybody protesting that the real thing doesn't have it.
But once a fictional thing becomes really popular, the fictional features become "real" enough that readers or viewers would protest if a writer changed an accepted part of it. In the case of The Necronomicon, for instance, the fictional author is "Abdul Alhazred", and any writer changing that does so at their own peril (and their readers' displeasure). Any movie portraying an "Acme" brand device as high-quality, useful and defect-free would similarly break a consensual agreement on what "Acme Corporation" should all be about. You can get to the point where the fictional entity is just as rigidly defined as any real thing. Terry Pratchett, writer of the extremely popular Discworld book series, has complained that his own fictional city of Ankh-Morpork has become so detailed through the years - with published maps and guidebooks, no less - that he has real trouble adding or changing things without getting called out by his fans for violating known "facts" about the city.
Of course, nobody actually tells you when they present a fictional place or thing as real. Many people probably assume that Teito University is a real place, and there's even people who think The Necronomicon is an actual medieval-era mystical book. It hasn't helped that there's several real books published with the "Necronomicon" title, purporting to be the real thing, it being a figment of Lovecraft's fertile imagination nonwidstanding.