ubiq: When we say Shulchan Aruch we include the Rema in that terminology. The Gedolim in the days of the Shulchan Aruch and shortly thereafter have agreed to accept the psakim of the Mechaber and the Rema as authoritative.
Regarding the Shach, the Shach writes that one cannot even claim “kim li” against a psak of the Shulchan Aruch. This is akin to accepting someone as your “Rebbi”, where you follow his psakim. This is the same thing that happened when, let’s say, Klal Yisroel decided that the period of Chazal has ended after the 7th generraiton of Amorayim (Mar Zutra, Mar bar Rav Ashi, etc), and nobody from here on in can add to the Gemora. There was no “halachah l’Moshe misinai” that told us that the Gemora was sealed; it was the accepted reality told to us by our Gedolim. The same thing applies to accepting the Shulchan Aruch and Rema.