Update 2: Wired got back to us. The official story is that they're not being sued, it was just a misunderstanding by Chen. But Wired has pulled the video after reviewing Apple's complaint about it.
Brian actually loaned his personal MSI Wind Hackintosh for the Giz Gallery. It seems more likely that Apple is actually sending Wired a cease-and-desist rather than asking for money—telling them to pull the tutorial, which explicitly lays out step by step how to put OS X on a netbook, including trips to The Pirate Bay to get the software, diving into the notebook's guts and other grisly details in a fantastic, super-complete guide to Hackintoshing a netbook.
We'll update with more details as we get them, but be sure to check out this awesome guide to building a Hackintosh netbook in the meantime—which is now sure to be seen by more people than ever before. Way to go, Apple.