>> If I take your picture, your image belongs to me. So it follows that if I take a picture of your picture, that also belongs to me.

As was pointed out in the article, only if its transformative in some way does copyright give you cover under the "fair use" doctrine:

Prince’s appropriation was “transformative” enough to qualify for fair use. In the words of the presiding judge: “[Prince’s] work adds new meaning...and the fair use doctrine guarantees [him] breathing space.”

A simple picture of a picture without alteration would still be considered infringement under the current copyright laws.