I think this makes sense. Filtered reviews are reviews that yelp considers to be fraudulent. They may be reviews created by multiple accounts from the same computer to inflate a restaurant's rating. Or they may all be negative reviews created by one person with multiple accounts to try to hurt a business they weren't happy with. Either way, I think it's perfectly reasonable that such a system of filtering should and does exist.

Now maybe their filtering system is so horrendous that it makes a 4-star restaurant seem like a 2.5 star restaurant, but I find this hard to believe.

As for asking people to advertise with them to make "bad reviews disappear", that would be terrible, so I can't speak to that, since all we have to go on is this particular owner's word vs Yelp's. Is there any proof of this happening?