I'm genuinely curious how you manage to find all these folks. I've been on the interview team at my company for a several years now(mostly in house, some first pass phone screens) and I've never encountered a single person who was literally unable to code a trivial problem. The last time I met a "programmer" who couldn't code was first semester university, and I thought most of them quickly flunked out/changed majors. I wonder if there is something about your company/recruiting process that is particularly attractive to them, or if our prescreen(which I'm admittedly no expert on) is just particularly good at filtering them out, or if there's some other explanation.
I saw him do SQL joins on the wrong column, cause accidents in source control, lose changes because he wasn't looking at the file and folder names on screen, and so on. Hard to realize for him, and hard to guess in an interview.