think your analogy of the Byzantine generals is a helpful way to understand the problem of trust in distributed systems. In the real world, there is no such thing as a trusted third party. Any third party that we could trust would have to be so powerful that it would be vulnerable to attack itself.
Bitcoin, on the other hand, is a decentralized system. There is no single point of failure, and no single entity that can control it. This makes it much more secure than a centralized system, and it also makes it more trustworthy.
The scoreboard analogy is a helpful way to understand how Bitcoin solves the problem of trust in distributed systems. It is a system that is secure, trustworthy, and transparent.