The Amazon Wish List can serve many purposes.
However, the only way other people will see it is if they specifically search for you using your name or email address - If you want it to be private, just change your name to something else, and link only the friends you want to see it using share, and let them know the reasoning behind changing your name so they don't think you're insane.
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That seems like something worth fixing.
Your profile is created automatically, whether you want it or not, and it contains comments, ratings, public Wish Lists, biographical information and other site interaction.
In theory, your Amazon wish list should allow people to buy you gifts, but should not reveal anything but the list of items you want.
I think this probably has to do with user privacy settings.
Many people use their Wish Lists for gift ideas, but we often use Wish Lists as a log of items we don't want to forget.