I think the challenge with finding firsthand reports on HN is that the owners of small brick-and-mortar businesses that Yelp is alleged to exploit are not well represented in this community.
Having said that, I have firsthand experience in having my own review of such a business censored:
6 months ago I wrote a review for the RazzleDazzle Barber Shop in Riverview, FL. Great little shop, I was surprised that it had zero reviews and was gray in Yelp. A month later, I returned for my second haircut and asked about business. I heard the same story about Yelp pressuring for sales, and mentioned that I had already written a 5-star review.
Upon checking Yelp, I noticed that the shop was still gray with 0 reviews, despite having left one a month ago myself. After carefully reading the site, I found that the keyword is "0 Recommended Reviews." At the bottom is a gray link that leads to more than a dozen reviews that are "Not Recommended", all 5-star, including my own. I wasn't the first to review the shop, the other reviews were hidden.
I wrote Yelp support to ask why this review was censored, despite my other reviews for other businesses being accepted. They assured me that an algorithm decides what reviews are recommended for protection of customers and that's all that's happening.
However, within a day my review was the only recommended review, and the barber shop was live on the site instead of gray. A few other reviews have been accepted since.
Go have a look for yourself, scroll to the bottom of that shop and click the "x Reviews that are currently not recommended" link in gray at the bottom. You will even find my original 5 star review, so perhaps they made a copy of it to get it to show.