OK, I've spent a couple of hours playing round with this and I think I know why it works for me, but not for you.
My GT is banned from the T10 servers, not from XBL
So when I play Forza on the second console as long as theres a Net connection the DLC shows up and is useable.
If I disconnect from XBL the DLC dissappers.
My guess is your console ban is from XBL as well as T10 which is why its not showing up for you.