I wasn't being very precise when I said that this would violate the RNC rules as well. The RNC has the same primary window which begins on Feb. 5th (but they actually have *no* exception for IA/NV/NH/SC). However, states can still hold their primaries before the window starts. They just lose half of their delegates if they do so. IA, NH, and SC are going to do this, and suffer the hit in the number of delegates they have. (And it looks like NV Republicans may join NV Democrats in doing that as well.) So it's not really against the RNC rules. You just lose a lot of delegates by doing so.
Actually, the SC GOP primary is currently scheduled for Saturday, February 2 which I believe keeps in within the acceptable GOP window. The parties run their own primaries in this state, so they don't have to both be on the same date and don't require any change in the law to be moved up. I fully expect that the SC GOP primary will move up a week to Saturday January 26 now, but they'll wait a bit to see if any other state might muscle in on their date.