Sounds like he was talking about the DLC stuff.
When you take off your HDD and put it on a different counsel, you have to be connected to xbox LIVE to use your DLC stuff, or else it either A) Doesn't show up, or B) Shows up as a trial/demo
This is because when you make your profile, it 'locks' the licenses to that system and when you pop it on a new system, it doesn't register it as the original. Pretty sure they do it so you don't scam them by downloading a bunch of DLC, switch to a new hard drive/system, and download it all again. Not sure, but that sounds about right

But yeah, if you want to keep your saves, just get a flash drive, format it for the 360, copy your stuff onto it, and copy it onto the new hard drive.
(I've spent plenty of time on the xbox.com forums with people saying "Whhaaaa! My dlc don't work!" with the answer always being, "So did you send your xbox in or get a new one?" "Yeah..." "Then do a license transfer, foo!")
~Cheers!