I believed Sol when he said that "...the other families will go along with anything that prevents a war..." (or something to that effect). So, in a non-Commission scenario, the attempt on Vito's life was a fait accompli by Sol and Tatt, with Barzini's encouragement. The other two families would go along because a war would interfere with their day-to-day businesses, and probably because Sol promised them a piece of the drugs business.