Xbox – GTA V Using someone else’s disc 1 to play the disc 2

Yes, with a few exceptions. Forza 3, for example, comes on two discs but one of the discs is data, so if installed, disc changing is not necessary.

The reason you need to insert each disc is a way of making sure you possess the physical game disc at the time you are playing.

It all started with this tweet from Rockstar official Support:

For optimal performance, we recommend not installing that disc. We will have more info on our Support Site at launch.

In their official support page they wrote:

I know Grand Theft Auto V has an 8 GB mandatory install. If I want to install the Play Disc too, through Xbox Home (dashboard), is that possible?

For optimal performance, we recommend only installing the Install Disc, and not also installing the Play Disc to the Xbox 360 Hard Drive or USB drive via Xbox Home (dashboard). You will be prompted to install the Install Disc the first time you boot the game.