WHICH "Sioux" refacer are you talking about? They've got a dozen or more models; some are bigger than others. The actual machine parks on top of a roller cabinet in most cases; the cabinet gets filled-up with the valve seat grinder, pilots, reamers, stones and stone holders, etc.
Mine is a Sioux 680. The original chuck with the "3 bullets" will hold wonderful runout (and works on valves with stems down to about 5.5mm). Half-a-thou, sometimes better.
The thing was FILTHY when I bought it (used.) I had to take it apart, clean the metal dust out of EVERYTHING, and replace the rubber motor mounts. Even the chuck was filthy inside.