You can control your fan comment or posts in Prvacy setting of your fanpage.

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I would totally make a public post addressing the person's complaints. Say exactly what you've told us. Maybe something along the lines of...

"Lately, we've noticed that a certain Mr. X has been making negative comments about this item. We welcome constructive criticism, but the strange thing is that Mr. X has never even bought our product. We've made hundreds of products, and we've barely had a couple of complaints- which we have addressed. We love our products, we believe in what we're selling."

This allows the person to respond directly, and if you play your cards right, the rest of your fans should hang him out to dry. Also, sometimes this sort of thing (if you're passionate enough) can go viral! Worth a shot. At worst, if nothing much comes out of it, you can followup and say that you've banned/blocked him for spreading lies.

Let us know how it goes!

-v

You can hide the post so only them and their friends see it, then proceed to BAN them.

It's your house.

If it was a person who bought your product then I would say to respond to the post. However since it is a person who did not buy your product I suggest you just delete the post and if it is made again ban the person. This person, if he has not bought the product, is just looking for 'drama' or trying to stir up trouble. If you respond at all you will just encourage them to continue.