Let's say you don't have access to XBox Live, but your friend does, and you want to download some mods or Arcade titles. Simplest thing to do is just pop off your hard drive (or a memory card), bring it over to your friend's house and snap it into his 360, right? The problem is that when you download a game, it remembers the actual base unit that paid for the download. It doesn't matter what storage device the game or mod eventually ends up on, whatever 360 was used to pay for it, that's the one that gets the permissions.
So what does that mean to you? It means that if you get something at your buddy's house, every time you want to play it at your house, you're going to have to connect to XBox Live first to make sure that you are, in fact, authorized to play that game. This comes under the category of "giant pain in the butt." The simpler solution is to just bring your entire 360 with you to your pal's, hook into his connection, and go from there.
Of course, the simplest solution of all is for you to just do it all at your own house. XBox Live Silver membership is free, after all, and with a little
creative thinking, you can access Live with plain ol' dial up.