Counterpoint: Name a great victory where top leadership mattered very little.

Or, for that matter, a massive upset where top leadership did not truly contribute significantly.

The "fog of war", AFAIK, tends to refer to general breakdown of communication (as you noted), but even fully localized control (terrorist cells, I suppose) are not highly effectual without coordination and informed assessment of the overall picture. The horrific triple (almost quadruple) attacks of 9/11/2001 would have been greatly diminished, probably by 2/3, if the attacks weren't centrally coordinated.

Wartime is exactly when centralized control is most needed.

In management, what it means is having to repeatedly make decisions that are in the best interest of the company, but not necessarily in the best interest of the people on your team. This could mean needing to fire people, conduct layoffs, merge teams together and remove redundancies, strip a manager of their direct reports or reduce their scope, replace a leader, drive a major re-org that changes people's jobs in ways they may not like, shut down an entire project or team that isn't succeeding even though it's very popular or well-liked in the organization, own a technical decision that hurts one or two teams but helps the overall organization enough to offset it, etc.