What are talking about? Who said the two Genovese men needed permission from Chicago to retaliate against Gotti?
They didn't need permission from Chicago to do anything.
They were sent out to Chicago right after the hit on Castellano. WHO KNOWS WHAT WAS DISCUSSED. The point is that the two men were not Gigante and Salerno. That's it. Nothing more and nothing less.
They were in and out of Chicago very quickly.

You have misunderstood about Grand Ave. I'm not saying there is nothing there at all. I'm saying there is no Full functioning Crew based out of that area.
Albie Vena is a made guy but he is NOT A BOSS like Caruso or Inendino with several made guys under him who have Soldier/associates working for them.