Unfortunately, Yelp's current model seems to encourage extortion at the hands of these third parties, and is also incapable of punishing them.
What I think happens / Paraphrase of what I'd imagine a 3rd party call to be like:
"Hi, this is Yelp. Pay us and we'll boost your rating/visibility and hide bad reviews. If you don't pay, your Yelp ratings will suffer."
Then they just manipulate ratings and review visibility with fake accounts. Add good reviews and hide bad ones if the owner paid, and add bad reviews and hide good ones if they didn't.
(Also I'm aware that there are plenty of "legitimate" businesses that provide this service and don't misrepresent themselves as Yelp itself)
I'm a Google Trusted Photographer in Houston and I visit and talk with businesses that get targeted every single day. I'm loosely affiliated with Google and I have to make that clear. They get calls twice a day from "Google" and "Yelp" about their pages and reviews. This is their #1 complaint when I call them or walk in their door. Being local helps.
Now, looking at such things from a common sense perspective makes it quite obvious what's going on. But proving the same in a court of law, which often will have a much higher requirement of proof, may not be so easy.
I wouldn't believe him if he told me it was pouring rain outside. I would check first and make sure it wasn't just a drizzle.
If you decline, the Yelp sales person could simply have their friend visit your business, have a "1-star experience" and then write a review.