I have personally done this on 3 consoles and it has worked fine.
Here is a quote from MS, they don't specifically state the problem you are having, but it is the same solution.
http://www.xbox.com/en-AU/support/xbox360/...playbackfaq.htmQUOTE
Q: I received a message that says a media update is required to play the content. When I download the update I get the message "The download could not be completed. Please try again later. Any points you used for this transaction have already been deducted from your balance and will not be deducted again" with error code 8070005. Explain.
A: You'll get this error if you previously downloaded the media update on another Xbox 360 console with the same profile. You are only allowed to download the update on one console per profile. You can work around this by creating a temporary Silver membership to download the update. Once it's downloaded, you will be able to use the update with any profile.
It really should work for you, as it has for myself and many others.