In any system, you can work out the easiest way for the system to betray its users, and then determine what resources it would take to do that and whether the payoff would be sufficient to justify the effort. A system will be safe provided it has the right margins between the cost to make the attack work, the benefit to the attacker of a successful attack, and the harm to the victims of the attack. Think about what would happen if someone who wanted to hurt Bitcoin managed to collect 51% of the mining power. With explicit trust, it's just as hard to accumulate 51%, but everyone else can just stop trusting all the entities they see cooperating in the attack, and the attacker has to start over from scratch.