Satire, and fair use of satire

I like this NYT article on whether the recent New Yorker cover is satire in a traditional literary sense. But the topic intersects with IP when it comes to other cartoonists' responses to the cover. The variety of ways in which they address the Obama cover demonstrate why fair use requires broad latitude in its targets and its approaches. Here's a link to a collection of responses. They are all clearly using the cover, but articulating how every one of them is criticizing the cover is harder (though, to be fair, easier than explaining why the original cover was a satire). Nonetheless, they're all obvious fair uses, even if turning the pictures into words is sometimes difficult. Here's a really easy one, which I like because it's an instance in which pure copying becomes criticism:

Bonus question: how do the cartoons that copy The New Yorker's name and/or font fare under Rogers v. Grimaldi and the like? Are they literally false designations of origin? Or would we want to say that here, there's no trademark use/use as a mark?