This one comes from GTAForums.org. User lazloisdavrock shared an email from Rockstar Games confirms that you will be able to install your entire copy of Grand Theft Auto V onto your Xbox 360 via its internal HD or removable flash drive.
The email explains that the game requires and 8 GB install off of Disc 1. Afterwards, you can choose to install the contents of Disc 2 (labeled the play disc) to the hard drive to keep a full copy of the game. Your Xbox 360 will require you to have Disc 2 inside the drive to run the game, but the console will run the play disc data off the drive and the disc will not spin. The game will fill out a total 15 GB on the Xbox hard drive, or a 32 GB external flash drive. What's implied here is the save data won't fit in a 16 GB flash drive.
Microsoft makes it a point to encourage game installs to the Xbox's hard drive, to make games run more efficiently on the system and reduce wear and tear on its optical drive. The optional install for Battlefield 3 adds high resolution textures. This feature will also be a selling point for the upcoming Xbox One, although the bad press it received over the used games DRM controversy may have obscured the possible advantages of this setup.
While we're still relegating this to rumor status, it seems likely that Rockstar Games would demo and add such a feature, as a test of the Xbox 360's capabilities, as well as for the benefit of fans. Cross your fingers that this one turns out to be true.