Shooting on-the-move is now essentially limited to moving to cover from an initial start position that is in-the-open. All other engagements are expected to be from cover.
I designed a stage for a sanctioned match that included targets that appeared (popped-up) after the competitor entered a Cooper Tunnel, forcing engagement while moving through the tunnel, since no cover was available, and was told, via my Area Coordinator's conversation with Robert Ray, that I couldn't do that. You not only can't leave cover to engage while moving, you can't design a stage that encourages it.
At the local level, I'm sure Robert Ray isn't looking over your shoulder when you design a stage, but the rules addendum removed the option of engaging while moving from one cover position to another.
I think it's an attempt to reduce "round dumping" via limiting the ability to run your gun dry while moving.