I don't think this is true from my experience. I've been on several program committees, and have managed a couple as well. Usually if you're above the first-level reviewers (e.g. senior PC, track chair, PC chair), you can see the actual author names and reviewers.
Most of the time when an author later says (formally through the review system, or informally in casual conversation) that "I know it's this reviewer who asked me to cite their own paper" they are wrong. Their main evidence is that the reviewer asked them to cite two papers that include the same author.
But of course I can't tell them otherwise because of the confidentiality, so they keep on believing that, perpetuating the myth. Perhaps someone can aggregate some statistics on this, but I genuinely believe that authors suggesting their own papers only about 20% of the time, and when they do it's because their paper was highly relevant.