But why is the issue so important? Because "action" is not just an ontological category. For ontology, "movement" would be enough, and it could be abandoned once one adheres to the contemporary subatomic paradigm, where rest is no longer the "normal" state of affairs.
Action is much a more an ethical and juridical category. To define what an action is means to decide whether one is responsible for it and, lastly, liable to be punished. In this case, sheer movement is not enough. One is not ethically censured for having moved one's finger, but rather for having shot someone. Hence, one would say that ethics adheres to Someśvara's idea of action as effort/volition (see this post and the immediately preceding ones).
On the other hand, jurisdiction does not count only the intentional, conscious side of the action, but also its movement-aspect. One is not legally guilty because of having desired to kill someone if one has altogether failed to do it (for instance, because one was still looking for a gun to buy as one's target died out of a car accident). Similar difficult cases are examined in chapter 5 of Vasubandhu's Abhidharmakośa. Notwithstanding his rigid intentionalistic approach, Vasubandhu also compromises with the actual performance of a bodily movement.