Oops...just a few days before the intended April 30 release of Canon's 1.2.1 firmware update for the 5DIII, it's leaked. EOSHD.com has posted a link to download the file if you'd like to install it on your 5DIII today. I downloaded the file from Andrew's site and am running it now on my 5DIII with no problems. Update when smoothly.
In my brief testing of the image recording to a Blackmagic Hyperdeck Shuttle verifies the HDMI is sending a "clean" out via the HDMI port. Initial tests seem to indicate that the highlights seem to be retained slightly better when compared to the in-camera CF card recording.