We couldn't find any of these users in our system, so we knew they weren't customers.
That is demonstrably poor reasoning. Anyone who puts their real name on yelp is an idiot.
What's more, most reviews were factually and demonstrably inaccurate.
Specious, and you've already demonstrated specious reasoning.
I hate to be the bearer of bad news, but you sound like a bad business owner, or in this case your friend is a bad business owner. You're demonstrating the telltale signs. Bad business owners often have a difficulty accepting responsibility. Bad business owners twist the facts to support their own side (you've stated that it not possible that these reviewers were customers). Worst of all, this business has attempted to retaliate against customers (I can see little to no reason to attempt to out the Yelp reviewers if not retaliation).
I have a Yelp account, and it's not in my real name. I leave bad reviews (and good ones). You could say I have a history of making bad reviews. You could also say that this business you are talking about has a history of receiving bad reviews. Yelp is far from perfect, but in business-friendly America, it's one of the most powerful tools we as consumers have to bleed dry bad businesses and bolster good ones. If this business wants friends' reviews visible, those people need to get more active on Yelp. That's it. That's the whole filtering algorithm as best I can tell. If you create a Yelp account for one single review, you get filtered. If you write more reviews, you don't.