Are the characters based on real people?
As far as I know, this is mostly due to the chara-designer's style, Inio Asano. He doesn't take his designs from real people (or at least he doesn't say so), yet his works all have this realistic and very diverse type of people.

As opposed to many anime chara-designers, he's not an animator, but a mangaka, with a very detailed, realistic style, as you can see below:





He drew the original chara-designs and character sheets that were used by the animators at A1-Pictures for The Perfect Insider, and that's probably that style you noticed. If you're curious, his works are critically acclaimed (and not only for the crazy art), with mangas like Solanin or Good Night Punpun.

Even though, you can clearly see how his raw style evolved to a more simple, and "round" style when it wad adapted, but it still keeps this realistic aspect. 

Hope it answered your questions, at least partially. Unfortunately, I couldn't find word from Asano on these specific designs.