Well, if you have two 360's then you would want to freely transfer DLC between them lest you prefer to buy the DLC twice. Given that the 360 is the least dependable console this gen, a second 360 is entirely plausible.
You can transfer your account to another 360 only once per year. If you got the RROD twice or more in one year (which seems to happen alot) then you would need to be online to use your DLC.
BTW, save files are usually dependant on DLC so if you have a save file with the Stone Prisoner DLC, then try to take your disc and save file (mem unit) to another 360, it will likely not load without that DLC present.
Now, I don't care if you approve of this type of DRM or not, but rest assured, IT IS DRM and you claimed DA had no DRM. It does, the devil is in the details.
BTW, on the 360 the DRM is in the console. So every 360 game has DRM, you just can't see it that well. Try to make a backup of a 360 game and then try to play it on your 360.