Earlier quoted context omitted.
I did... unique among their database...
You may be unique, but within a very small pool. For example, my current user agent string alone narrows me down to within one in ~2-3 million users/browsers. When taken with the intersection of all those other bits, it's very easy to get an incredibly high-resolution snapshot of an individual...
I used Panopticlick, and no one else who has used Panopticlick had the same fingerprint. The meat of the uniqueness was in Browser Plugins and System Fonts. Think about that... If you've installed a few random fonts you found online, you're probably sending a unique font signature. If you've grabbed a few plugins, messed around with extensions, then you're probably sending a unique plugin signature.