Stress relaxation dynamics of model branched homopolymers with a range of architectures (A(2)B (T-shaped) and AB(2) (Y-shaped) asymmetric stars, AB(n) (combs), B-2-A-B-2 (H-shaped), and B-3-A-B-3 (pom-poms)) are studied using a tube-based theory to evaluate a recent proposal for branch point motion in hierarchically relaxing branched molecules. This model contends that if the random coil size R-g,R-B of relaxed B arms connected via a branch point to an unrelaxed Z(A)-mer polymer backbone is larger than the equilibrium tube diameter a, the branch point can only move a small distance delta = (ap) of order a/ root Z(A) during each relaxation cycle of the arms. When this prediction is integrated into tube models for branched molecules, it yields a self-consistent theory suitable for describing linear viscoelasticity (LVE) of any branched polymer system. Without artifices, such as arbitrary adjustments of the measured molecular weights, arm functionality, or dilution exponent, we find that this theory yields LVE predictions that are consistent with experimental data from many groups.