This is false. Source: I worked there, on search. You cannot pay to rank higher in search.
You can argue whatever you want about your former employers but convincing SBOs that Yelp aren't extortionist scumbags based on this detail is not going to fly.
Source: I work directly with maid services and trust in Yelp is at an all time low. Literally the first comment when they are mentioned in our private group is something along the lines of "Die in a grease fire" or "F*ck Yelp". And this is from some of the nicest ladies (mostly) that you'll meet.
No, it's a common rumor. Repeating rumors does not make them true, and this "knowledge" is completely false.
I have no financial or business interest in Yelp. I just don't enjoy seeing my own work, and the work of my colleagues, disparaged by completely unsubstantiated rumor mongering.
Yelp is also terrible for owners who purchase a business and are strong armed into doing business with yelp on order to remove all the previous bad ratings, description, contact info, etc. (Source: bought 1 bar in LA and 2 in LV)
ads from paying businesses list higher than search results; this effectively means you pay to be "indexed" higher
Their sales tactics are borderline abusive, too. They will hunt you down forever until you sign a package with them, and they give you zero time to think about whether their ad package (which only works on their site and has a super high CPC compared to AdWords) is right for your business.
They need to go away