Back on the xbox 360, there was a more involved process to do the same thing. A digital purchase really granted two licenses: one tied to your account and one tied to the specific 360 that downloaded it. My sister and I took advantage of that to share season passes for various Call of Duty games.
Useful trick, although I first discovered it when visiting family, buying a game on my account and then wondering why I couldn't play it offline back on my own console.
