It's a nice thought but is there any evidence of this? I've also heard this quote "If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you don't quite know what problems are worth working on."

In my experience at work, I've seen the opposite. The people most distracted get the least done and it's obvious to everyone on the team. Plus obviously you do need to pay attention to some distractions. Going too far in one direction is not good. I think, however, most people lean more towards distractions than focus.