Eric Wemple of our sister institution Washington City Paper explains what happened with Huffpo asking them to pull their parody, which is back up for now. Their objections were apparently 1. the page still had active blog feeds and 2. it linked to Huffpo. In other words: huh? So for now parody is safe, although the irony of a publication that relies on, um, generous fair-use interpretation and justifies it with arguments about linking objecting to a vastly more conservative version of same is now all the richer. Everyone wins, insofar as one can in this brave new world.
Update: David Carr has more, including a note from WCP editor Erik Wemple.