One thing that Yelp absolutely does do, I've seen it with my own eyes, is play with 'recommended' reviews based on whether the business in question is paying them. I can't provide hard links because it's a client of my wife's business.
Specifically, a business had about 20 very positive reviews in total, all of them 'recommended'. A review that isn't 'recommended' basically doesn't exist; it doesn't count toward the average rating and it can only be viewed if a small print, difficult to see link at the bottom is clicked.
So, a business started with 20 total rating, and all 20 of them 'recommended', with a very good average rating.
Said business decides to send some money Yelp's way; that goes on for a few months, and they get a minimal uptick in hits, but worth less than what's being sent to Yelp.
So they (within the contract with Yelp) stop that relationship.
Shortly after, 75% of the reviews switch to 'not recommended'; the ones that remain are among the lowest ratings. The new average for the business isn't terrible, but it's lower.
Multiple calls to Yelp are all handled basically the same; "That's just an algorithm and we don't really control it." ... "I think if you re-establish your contract with us, you might get more business."
The language on the phone is tricky; nowhere is a direct connection between sending money and 'fixing' the Yelp score mentioned. But it's heavily implied. When asked directly, they just deflect talking about the opaque 'algorithm.'
That was the most recent case my wife dealt with. There have been at least two other fairly similar situations.
At this point, she's telling her clients that it can be dangerous to engage with Yelp if they haven't already done so.
TL;DR: Yelp is shady as hell. Full stop.