Rather my upthread argument is that Byzantine fault tolerance requires the ability to distinguish between a fault and a non-fault, because otherwise the system does not present the same symptoms to all observers (which is a requirement of Byzantine fault tolerance). Satoshi's PoW can't distinguish a fault (attack) from a non-fault (non-attack).
Byzantine agreement is the process of forming a consensus decision on truth in the face of faulty network participants; bitcoin achieves this. Your definition of fault is incorrect in this context; a fault is information which the majority doesn't accept as truth, which manifest themselves as orphaned branches in bitcoin. Obviously all observers of the network can see orphaned branches.