First of all, Accardo was never THE BOSS, he always reveled in his role as consigliere. He held the underboss position for a short period of time (on several occasions), but he was not a fan of the responsibility.
That sounds reasonable, but it is generally believed that Ricca and Accardo were the ones who called the shots. Maybe Ricca was the top boss for some time, but Ricca and Accardo were said to be very close friends so it didn't really matter.
"It was between the brothers Kay -- I had nothing to do with it."
