That's the problem with mass communication, isn't it? And it's why the deconstructionists got a foothold in the English Lit. departments and (from there) into the interpretation of biblical and other ancient texts.
The fallacy in deconstructionism (such as my simplistic mind understands the philosophical mumbo-jumbo that surrounds the concept) lies in the belief that simply because a reader can misconstrue the intent of the artist, the intent of the artist cannot be discerned and thus the reader can be excused (or even encouraged) for giving whatever interpretation he or she wants -- thus "owning the interpretation".
I don't subscribe to that point of view, as I think my comments on poetry (including sung poetry) here should make clear. The artist has a responsibility to make the intent clear, and the reader has a responsibility to seek out the intent of the artist. Both sides have to do their part, else mass communication is impossible. So I would say that neither takes precedence. (It's no surprise to me that in our "democratic" society, Miller would say that the reader's point of view takes precedence. In an authoritarian society, it would be taken for granted that the artist's point of view takes precedence -- consider how the Soviet Union used art and artists in the service of the State, with the reader's viewpoint being expected to conform to the artist's intent.)
That said, not being a regular reader of The New Yorker I was actually wondering at first glance if their satire was meant to express their own views of the Obamas or someone else's -- views that certainly express the fears and accusations of many a tangential conservative. Somehow the context didn't "jive" with the content. That (as Yoda might have said about the magazine's artist and editors) is why they failed. A magazine as relatively "liberal" as The New Yorker shouldn't have to explain itself when it puts up a caricature of conservative fears and accusations, and I believe the fact that it must says as much about the editors and the artist as about the readers.
wr ()()