I think productivity has more to do with "do I actually care about what I'm doing?" and "do I have any real interest in being productive?"
Concur, in certain situations. In others, no amount of "work harder" can trump "work smarter" for total productivity... particularly in circumstances where the "product" is information-based (a design, a story, a program, a solution, etc.).
There are other situations in which the process is prescribed, and there aren't many opportunities for time gain. For instance, no matter how smart the pilot is, the pre-flight checks are the pre-flight checks, and the plane is only going to travel as fast as it travels. A super-smart pilot might find ways to shave a whopping ten minutes off a 6-hour flight. That won't make him more productive, it'll just get him home ten minutes earlier.