We argue directly from Witten's analysis of large N(c) baryons that the structure of the s-wave low-spin baryon states in QCD becomes spin-independent as N(c) --> infinity. This property leads to an SU(6)-like behavior of static matrix elements, such as the axial-vector vector current matrix elements recently studied by Dashen, Manohar and Jenkins. Our analysis suggests a method for applying large N(c) results for N(c) = 3, even though the baryon states for large N(c) are very different.