I'm still of the opinion we shouldn't bump the stat trio up
It's not as if that one person has absolute control of everything, there will no doubt be other people who advise on/carry out orders so there is a limit to how bad the actual performance is - not all of these workers will carry out stupid tasks.
There are also other factors:
Morale, tax, cost modifiers, public order, health, farming, law. The list goes on. Command, Management and Influence are just generalised traits but are in no way total in their portrayal of the actual skill and ability the character has. A character might actually be terrible at commanding armies effectively, but he is such a likeable, loved and fair leader that the people would fight to the death for him. 0 command perhaps, but +3 morale.
A character could be pretty bad at handling money in general but he is very good at making sure the right personal work in the right job. He might also be very good at propaganda and thus this character might have 2 management points, but makes up for it by reducing construction costs by 10% and recruitment cost by 20%, reflecting the effective targetting of the work force and the reduced cost of trying to hire people for war.