343 Industries has revealed that they are not working on a HD version of Halo 2 after all.
Last week OXM UK reported that a remake was underway, but 343 revealed that they "are not working on that at this time. We are kind of busy," when quizzed during an interview on Halocouncil.com (thanks Izrael).
However, it is worth considering that much of Halo Combat Evolved: Anniversary was outsourced to other companies (most notably Sabre Interactive), and it's entirely possible that the same is happening again.
A 2013 release would fit the pattern of near-yearly releases established by Microsoft with 2007's Halo 3. And 343's assertion that 'We are not currently working on that," might be technically accurate, but whether it's true remains to be seen.