It's not that we don't trust things that have just recently been tossed out of the ocean, but signs point to this rumor in particular having been in a tussle with a remarkably violent manatee. In other, less ridiculously analogous words, previous comments from Microsoft don't quite support it. Just last month, Microsoft rubbished claims of an Xbox 360 with built-in HD-DVD drive and before that, they remarked that "you don't need HDMI for HD gaming."
With a seperate HD-DVD drive and the format's Image Constraint Token supposedly delayed until 2010, reasons for an HDMI-capable Xbox 360 (instead of first-party converter cable) become quite nebulous, at least if Microsoft doesn't plan on annoying early adopters of its spinning system. We've contacted Microsoft and, barring the usual "we don't comment on rumors or speculation" reply, we'll be sure to let you know whether or not you can believe some things spurned from the sea.
[Via Engadget, thanks to everyone who sent this in.]