Even if you remove cookies, you can still be identified. Your browser is very, very leaky with the information it provides(probably by design, since all the major web browsers are in the pockets of the worlds largest ad distribution networks, one way or the other).
That's actually why I included a note on removing or severely limiting headers sent like user-agent strings. There are occasional uses for those when there are actually client-specific differences, but those are few and far between outside the embedded space.
Add it to the list of obvious examples where browser vendors are disingenuous. Saying they care about privacy while sending a long list of identifiable information is disingenuous at best.
