Steve,
The Israeli regime was responsible.

It was indirectly responsible, because it was the controlling power, but it played no role in the massacre.

Sharon's head rolled and he was the defence minister.

Again, only indirect responsibility.
Wiki,
"Israeli Defense Forces were indirectly responsible for the massacre since IDF troops held the area.[65] The commission determined that the killings carried out by a Phalangist unit acting on its own, but its entry was known to Israel and approved by Sharon."
"The commission also concluded that Sharon bore personal responsibility[65] "for ignoring the danger of bloodshed and revenge [and] not taking appropriate measures to prevent bloodshed".

That is Israel's version of events.