I guess Young could factually prove that Rush framed him for a murder that was in reality a suicide, but Young is in charge and it's not a democracy. I can't really imagine Shep or O'Neill not doing the same thing. And if Rush had obeyed orders from the start none of them would've been on Destiny to begin with.
Yeah, Young is in charge and it's not a democracy - because Young says so. He basically set up a military dictatorship. It's no wonder there was a mutiny.