One can fill their days by completing many mindless tasks and consider themselves as productive, but in the end hardly any of those tasks really matters.
On the other hand, another person may only complete one or two tasks in a very short time during their day but these were critical tasks that could generate much higher values. This subsequently makes the person more effective than their peers.
The output values must be weight in determining if one is really productive. Effectiveness triumphs mindless productivity.
This is quite similar to the cognitive and decision fatigue principle which indicates that each of us only has a limited pool of cognitive resources and so we must be very selective in choosing what activities we engage in.
To remain highly effective, not just being productive, particularly for a project manager, it's imperative to spend time only on tasks that require critical decisions to be made, and to delegate the rest. When you take on more tasks than you can handle, like some are misunderstanding this may help them appear as productive, it will undoubtedly affect the quality of each of your decisions and the project will suffer.