That's not the only way to lie. You could, for example, lie that a transaction that doesn't exist has gone through – say, in a cross-chain “currency exchange”.

That's not the only way to lie. You could, for example, lie that a transaction that doesn't exist has gone through – say, in a cross-chain “currency exchange”. Or perform a double-spend attack. Or many other things, because the Byzantine fault tolerance doesn't apply in this case.