This intriguing question is on the same par with "does anyone really know what time it is" and other mind benders. It's not really possible to do nothing, as the body is always doing the autonomic work of staying alive. Even a Zen master must work very hard for years to reach the deep meditation state of nothingness for a short period of time. So, yes, doing nothing is something that might take a lot of work.
To choose not to act where one could do something is a choice. A choice in an action. An action is, in turn, something that a person does. Since a person chooses to do nothing, he is acting. Although doing nothing is not the typical idea of what doing something is, it can be.