I don't think the NG (or CL) prohibits takeoff with V1<Vmcg. All of my performance manuals say the same about increasing V1 to Vmcg.
My thought is that maybe the CAP changed with the new definitions/certification and they neglected to mention that, "You can't take off with V1<Vmcg but you can just increase it to Vmcg."
It's kinda like saying "You can't take off with snow and ice adhering to the wings" and forgetting the bit about "but you can de-ice."