By even going to the site, you are giving them data.
They have your IP address, the unique attributes of your browser, etc. etc.
Once they figure out the profile is fake, they list you in the "trouble maker" category and step up monitoring that IP/browser combination until they know who you are, then they link that with everything they have on the real you (bank account, property, job, etc.)
Eventually, one day, you're trying to board a plane and you get denied because you've been known to disseminate "false or misleading information".
What unique aspects of your browser? The User-Agent header will tell you the kind of browser you have. However, it's unlikely that you are using a browser that's very unique.
They can use cookies to identify you. But you have to keep going back to their website.
You know, I've been to this site several times, but noticed just now that it says "1 in 27588" about plugins of *stock iPad browser". This seems to be off, way off.
You don't have to go back to their website very often; your browsing is tracked every time you visit a page that has a 'Like' button. And as others have noted many people's browsers already have a unique fingerprint even while you are logged out of Facebook
Once they figure out the profile is fake, they list you in the "trouble maker" category and step up monitoring that IP/browser combination until they know who you are, then they link that with everything they have on the real you (bank account, property, job, etc.)
Eventually, one day, you're trying to board a plane and you get denied because you've been known to disseminate "false or misleading information".
Playing their game validates it. Just don't play.