Accardo was a boss before Giancana. This isn't from Roemer, this is from many different informants including members of other Families, as well as recorded conversations. Accardo sat on the Commission before Giancana did and was recorded explaining protocol to Giancana when he was a new boss. Before Accardo was the boss Ricca was and he sat on the Commission, the difference is that while Ricca was the boss Lefty Campagna was considered the top Outfit boss. Accardo became acting boss while Ricca and Campagna were in prison, then Ricca retired and became an adviser, and remained an adviser until he died in 1972.

In 1956/57 Accardo retired as day-to-day boss and became an adviser like Ricca, but Ricca had seniority. Giancana was the day-to-day boss until he retired to Mexico in 1966. No one considered Giancana an idiot. He was respected by all Outfit guys but not everyone liked him. Aiuppa and Cerone didn't. When Giancana returned I don't think he tried to become boss again. His main backer and protector was Ricca, and all the Taylor Street killings happened after Ricca died. Other killings include Richard Cain and John Rosselli. Cain was an informant and may have been discovered, but it seems that he was alleged to try to take over the Outfit too. Giancana was Rosselli's protector, but with Mooney he had no protection and wasn't liked by Aiuppa.

As for Blasi killing Giancana, there's another theory that Blasi let the killers in, but he wasn't an actual shooter. This one makes the most sense to me. Joe Fosco talks about it.