I have heard of a switch that has to be selected on Xbox 360 cables to get HD resolutions, but it may have been the Microsoft HDMI cable.
The standard cable that comes with the premium has component and composite output cables. There is a switch on the cable itself that has SDTV/HDTV on it when you are using the component cables. The X360 knows which cables are in it though (mine can tell the difference between component and VGA cables plugged in). So I don't think it would even ask you what resolution to output if the cable was set to SDTV. I think this is more of a TV problem.