The difference between South Park and this cover is this - the viewers/fans of South Park see the satire in the context of their knowledge of the show's genre. The cover of New Yorker is seen by casual people. As someone else suggested, if the cartoon was inside the mag along with the article, this would be a non-issue. Again, I can appreciate satire most of the time but I see neither humor nor satire in the picture. He put all the pieces in there but (to me) failed to depict it in a way that implies a mocking of those that accuse the Obamas of what they are not.
BTW, I did not find that Horsey cartoon funny either.