DLC is tied to the console and the gamer tag. the only problem you will run into is when you have no connection to XBL on the console does NOT have the license for the console. you will not be able to use the DLC if you have no internet connection in that case.
ran into this when i got a 2nd xbox for the house.
and its not so odd a question... maybe thats what they are doing, maybe its not... with the info provided, you dont have enough to say either way.