yes, sometimes
From FF/WF's new tab page in 'private' mode:
"When you browse in a Private Window, Firefox does not save:(visited pages)(cookies)(searches)(temporary files)
Firefox will save your:(bookmarks)(downloads)
Private Browsing doesn’t make you anonymous on the Internet. Your employer or Internet service provider can still know what page you visit."
So it stops short of indicating Tor but does imply there are things for which the browser can't just switch on easy fixes. If people don't understand, it's just as was already said: they don't read. Or they don't have that modicum of trust in their own ability to interpret correctly, so they don't even try, defeating the purpose of authors simplifying it ITFP...