Safari on iOS certainly does have "private browsing". Just go to the Settings app and select "Safari" from the top level and it's the first setting under the "Privacy" (just below the "General" section). When it's enabled, the browser looks different to let you know -- the normally gray bezel UI becomes black. This has been a feature ever since iOS 5.0 was released in 2011.
More info here: http://support.apple.com/kb/HT1677
Which sort of makes sense - the info it's looking at is basically the header info. Screen size, installed fonts, IP address, and so on. It's not relying on cookies, as cookies can't be seen/read across domains (you can't tell I'm an Amazon customer if I just visit you out of the blue).
CSS may color visited links red, but they hacked getComputedStyle to return the normal color instead. So, you can't tell if that link to Amazon you just created is visited or not.
And you can no longer set, for example, font-weight:bold for visited links, because that would change the size of the element, and they decided, unlike in the color case, that it would be too complicated to get all the APIs to lie about the new geometry.
All the site doesn't mention anything about IP address on the report page and presumably doesn't have access to third party tracking cookies however so private browsing shouldn't make much difference (I cleared my cookies and got the same score).
In the current model real privacy can only be achieved running something like Tor.
I haven't done the math, but I have a feeling it just keeps dividing by the "one in x browsers have this value". Maybe it doesn't look at the intersections , for example: Using Totem as the default wmv player is rare and using Ubuntu is rare but reporting Totem as .wmv player is going to be a lot less rare amongst Ubuntu users that it is amongst Windows users.
Why would it have to use division, or for that matter, any kind of math at all? I imagine that as each new visitor is recorded, they simply count how many other visitors had the exact same browser configuration.
The "one in x browsers have this value" column is probably just for informative purposes (and not the raw data that was somehow munged to determine the uniqueness of your browser fingerprint).
My previous comment on this: http://news.ycombinator.com/item?id=4479876
but still: so I'm only as unique as any iPad users in GMT-7, not all iPad users globally. That's not information that is of any use in identifying me, but EFF insists on presenting it as though SWAT teams from adwords will be breaking down my door any day now to shove targeted marketing materials down my throat.
Since the iPhone 5 makes up more than one in 200,000 of the Internet's traffic, even that "relatively low" uniqueness is worrisome.