The startling result of  that the number of very strong Mgll absorbers (with equivalent width of the blue component bigger than 1 Å) along gamma-ray burst (GRB) sightlines is nearly four times larger ([dN/dz/ GRB = 0.90) than that along quasar sightlines ([dN/dz/QSO = 0.24) has yet to be understood. We reconsider the possibility that the excess of very strong Mgll absorbers toward GRBs is due to an origin intrinsic to the GRBs testing for possible differences in some properties (line profile, dust abundance and kinematics) of very strong Mgll absorbers found toward GRBs versus those found toward quasars. With a variety of comparisons of equivalent widths of numerous transitions and of the kinematics of the Mgll profiles, we find no significant differences between these samples. This implies that if the excess of very strong Mgll absorbers toward GRBs is caused by a phenomena in the local GRB environment, that the process involved must have some similarities to that which produces very strong Mgll absorbers toward GRB. Although we might be inclined to refute an intrinsic origin of the GRB absorbers, we note that many narrow absorption line systems intrinsic to quasars are quite difficult to distinguish from intervening quasar absorbers despite an obviously different physical origin in accretion disk winds.