Though I agree with your points for the most part, let's not forget that the president does have real power to directly affect policy in this country, as well as shape key parts of government, as we are all being constantly reminded of lately.

But let's also step back and recognize that "the president" has always been at least the president himself and his adminstration. Of course the network expands from there and the key employees that you mention in important companies include individuals capable of weilding considerable 'asymmetric' power.

Lately, I can't help but think of Cigarette Smoking Man.