Headhunters that won't tell you the companies name

But I also think that undefinable aspects play a role. The interviewer and future employer likes someone or not: For having the same hobbies, for having a nice chat, or just having a pretty face. Body language, tone of voice.

While that is a possibility, I wouldn't rule out that the recruiter is professional enough to get past that.

I wouldn't put much stock in what the given reason is if an applicant is turned down; I most likely wouldn't tell the (whole) truth, either. Of course, hearing something like "the vibes weren't there" is frustrating, but the bottom line is that you don't know who you're competing with, and on which level they were judged to be better, so there generally isn't much sense in getting upset about it.

Let us forget that a company is made of people. Let us not assume that they don't mistakes.

If candidates can cheat so can company/recruiters.