I always thought private browsing was just so all the porn content doesn't stay in search history's and the address bar doesn't auto fill fatasshonkeybabes.com if my grandmother sits down to look at her Facebooks.
And it was always clearly stated as such. It's absurd that anyone was upset by this. I have yet to find a single user on here who did not properly understand what it was for, or at least none willing admit to being that dumb.
Private browsing in Google Chrome will not store your browsing data locally into your computer; but Google will still keep that data in their own records.