Column subset selection, choosing k columns of a matrix A that capture its dominant behavior, underlies many problems in numerical linear algebra and data analysis. The classical Golub–Klema–Stewart (GKS) scheme selects these columns by pivoting on the leading right singular vectors of A. We show that a pivoting strategy due to Stewart, building on work by Bischof, computes a strong rank-revealing factorization of any matrix with orthonormal rows. Combined with GKS, it achieves rank-k approximation bounds matching those of a strong rank-revealing factorization applied directly to A. We extend this framework in two directions: an analysis of GKS when only approximate right singular vectors are available, and a randomized variant of the pivoting strategy that retains the same guarantees while running up to two orders of magnitude faster.