Even for journal publications, the reviewers are anonymous. So really there is no reason to not just express your true opinion on a submission (as a reviewer). I have literally approved for publication dozens of submissions from unknown universities and non-affiliated contributors.

It is extremely hard to believe that the submission was not accepted BECAUSE of the lack of university affiliation.

But what is indeed true is that different conferences/journals have different expectations from a submission. Some prefer more theoretical analysis, others more computational work and benchmarking. And this is where a seasoned Professor offers value. They can judge where to submit a paper and have a high probability of success.

The conferences to which I've submitted papers have all had blind review -- you literally take your names off the paper and reviewers don't know the authors. Like OP, I don't have an academic background but it's been immensely helpful to have a PhD as a coauthor, as not only does he know all the conventions about paper-writing, he's also a wiz with LaTeX.

Exactly. The reviews where blind in my case (even thought I heard that's not always the case, specially for journals). In my case, there were multiple problems, like missing proves (probabilities and examples are not enough), which I agree. A lot of great feedback! Actually in retrospect, it seems amazing on how much feedback I got. Only one of the 6 reviews was about the tone, and rather useless.

Reviewers are also often quick to dismiss a paper when it hasn't done its homework of thoroughly reviewing all the related literature and explaining how the proposed result compares. This may seem pedantic, but it is important to limit reinvention of the wheel, and to give credit where credit is due (academia runs on credit).