Doom 3 BFG Edition prevents access to Doom and Doom 2 when Doom 3 is installed on the hard drive. According to publisher Bethesda this is not a bug.
"Doom 1 and 2 are the same games that are currently available on Xbox Live. Installing Doom BFG files to the system's hard drive could cause a conflict with the existing XBLA game files," a Bethesda spokesperson told Joystiq. "Players should not see a performance advantage by installing Doom 3, so we recommend not installing the game to the Xbox HDD."
They added, "If people do install DOOM 3 BFG Edition to their hard drive, they should still be able to access both titles from the Xbox Live Dashboard under 'My Games'."