We didn't get our Beta in the ODST disc. Yes, after you download the Beta, your ODST disc is not necessary anymore. You gotta go to your Games Library, and browse for a "Halo: Reach Multiplayer Beta".
Don't start up ODST. Go to the Dashboard. Go to your Game Library (next to the My Avatar pane) and look for Halo: Reach Multiplayer Beta.
I have the same problem. Id love to not have to put in the ODST disk but the beta doesn't show up in my games library. The main reason is because my disk drive takes about 10 minutes to detect the disk, thats after I have opened and closed the drive countless times.
Insane did, and pretty sure BT did as well. Fail by both of you for not realising that's why it was . F&F got a slightly different version of the Beta file, one which doesn't need to be accessed via ODST because it was downloaded directly using a code, so having to use ODST wouldn't make much sense. The regular Beta downloaded via ODST needs the disk in the drive to be played, otherwise there would have been less of an incentive to buy ODST as people could just go around installing the Beta on all their friends' Xboxs.