Am I right in presuming you have a legit version of the game (not burned) however can't go on Xbox Live for some reason?
What you linked to for changing the media ID should work if you have a Jtag / RGH hacked Xbox 360 as the title updates for most games are pretty much the same, discs from different regions have different media ID's so require the title update to have that media ID. For a non modified Xbox 360 you can't edit the title updates, as it breaks the signature, essentially meaning meaning the Xbox 360 will see it as corrupt.
How can I change media ID on the updates? I'm still trying to wrap my head around changing media IDs for the XEXs.If you update a RGH with a normal system update it will brick the console, however the Ethernet port is useful for playing system link games and copying content to the console over FTP, so that seems a bit of a strange thing to do. As you have an RGH i'd honestly try changing the media ID on one of the system updates you have found and see if that works for Forza 4.