Private browsing still lets your browser show cookies that it already has, it won't store new ones (except it doesn't have control over plugins, so they might).

What that means is if you are a regular Amazon user then decide to pop in as a stranger by turning on private browsing, Amazon will still know you.

What Private Browsing does do, is on window close get rid of all the cookies, history, field autofills, and such that you accumulated in two hour private browsing session searching for an opened, boxed, Luke Skywalker figure for your girlfriend. It doesn't stop the web sites from keeping track, for instance eBay might still show them in the recent items if you were logged in.