"Control" may be too strong a word. The Outfit had varying degrees of influence over the families west of Chicago. And one of the main reasons the Genovese family has always been considered the #1 family in the country was/is because of their control of labor unions and influence in legitimate industries. More so than any other family.
Agree, however it's the Chicago Outfit's role in politics and corruption, urban legend or real that makes me put a lot of weight behind it.
Obviously the Genovese has always been #1, but it's typically the Gambinos that are compared to be the runner up, where I don't think that was always the case