Yes, you are correct.
As per Philip Carlo's biography, Tony Ducks and Christy Tick had a private meeting with the Chin to discuss Gotti. Some others, like Casso, were waiting in the other room to hear what the plans were. They emerged and shared the news that they were dispatching the Genovese Jersey crew to handle the job.
After the Commission trial left Amuso/Casso in charge, they now met directly with the Chin. The Genovese Jersey crew was unable to get to Gotti, and now the Chin delegated the job to Amuso/Casso.
That's fascinating. In the distant past, when a Boss needed to be taken out, the Commission would give some faction from within his family the sanction to replace him. But in the above scenario,
it actually looks like the Genovese and Lucchese mobs wanted to whack Gotti and divie up the Gambino rackets amongst each other. 
