While it is true that anything you don't exercise will atrophy, like you said, but - at the same time - you can't be a master at everything.
The person that can be a master programmer and a charismatic salesmen is very rare indeed. In fact, so rare that I would be surprised if they exist at all.
So I agree, you shouldn't completely ignore tasks that don't fall under your speciality; but also, work on those tasks only enough to maintain a certain level of competency and skill. Then you can hopefully stay in touch enough and not "loose sight of the company as a whole."
For example, if you're a "technically-savvy, introverted programmer" and you hire in a "outgoing marketeer" to handle all the customer relations then you may find that you loose touch with customers and loose sight of the company as a whole.