Being busy doesn't really equate to productivity. Some people are always busy but don't have an output, or if they do, it's not of good quality. Google definition of productivity is the "effectiveness of productive effort, especially in industry, as measured in terms of the rate of output per unit of input". This only means that if you do not have a quality output by the end of a "busy day", then you weren't really productive.
I work in a government research institute where a lot of people say they're busy, one of the bosses especially, but do not really accomplish anything. They come to work at 6am and go home at 6pm, covering a 12-hour work shift, even though normal work hours is actually 8am to 5pm, show (and tell) people they're working on something and that they are not to be disturbed, for two weeks, but by the end of their "busy period," they still haven't accomplished anything. And then the boss on top of that boss gives the same assignment to someone else who was able to do it in three-days time without having to come in at 6am and go home at 6pm.
What i'm saying is, productivity is more equated to efficiency than being busy.