The OEM restriction is for motherboards. If you changed motherboards, you'd likely have an activation issue.
Although there are reports from time to time that Microsoft can be forgiving about new motherboards---apparently acknowledging that motherboards do fail and that an OEM shouldn't prevent you from replacing a motherboard, particularly with the exact same model.
MS apparently handles motherboard/OEM issue on a case by case basis, depending on who you plead your case to over the phone.
But I've never heard of any problems with a hard drive swap.