I can use existing products to identify your particular device even in a completely encrypted connection; if I can see the requests' content, I can tell even more, regardless of user agent string. And if I can see the requests, I can probably inject a response, which allows for a large range of probes and attacks to further identify your device. Worst case I can even use your latency to identify where you are.

Privacy means that nobody but you and the site you are visiting have your private information. Anonymity means the site you are using has no idea who you are. They really need to clarify these things.