what a funny situation! I never needed to log out because I surf Amazon.com from home, but now, when I think of people who, let's imagine, might have to quickly order a couple of books from the office and then to log out. It may become quite a mess. Interesting issue you pointed over here, watchinYou.
I have two correction though:
1) The page, to which brings you the link "If you're not..." doesn't contain link text "click here" for logging out, as claimed LazyJim. There is a link "Forgot your password? Click here", but not "to log out". At least, I couldn't find it. Maybe the assumption is that I get both text fields cleared, but they aren't.
2) This whole line is located there on the Home page only.
It must have be done on purpose, because I think that Amazon are very good at usability. Both - user experience and GUI.
Is there any chance it is a omission that we're talking about?