Facebook threatens to sue man who changed his name to Mark Zuckerberg

It seems like this guy violated Facebook's Terms of Service, so they shut down his account. I don't understand how violating Facebook's ToS gives Facebook the right to sue. I was asking about that legal detail.

If a business were to pay 5000 third-party individuals to "Like" a page, that business might not have a Facebook page and may have never agreed to the Facebook ToS. In such a case it seems to me that Facebook's only option would be to shut down the 5000 accounts who posted fraudulent Likes.

How does one distinguish a fraudulent Like from a true Like? If someone gave me money to Like something, I might go check it out, and actually, truly, like it. Then what? What if I Liked the thing but gave the money back? It seems to me that a judge or jury would have to decide these things, after gathering evidence and testimony, and there's no way to scale that.

Obviously Facebook will be able to find the businesses offering to pay for Likes, but I don't see how they can go after them (legally) if they have no direct connection to Facebook.

(The 'Like Store' in this story did have a direct connection to Facebook, so Facebook was able to shut that down and able to invoke the Facebook ToS.)