Since Bitcoin can not detect faultiness (consistently provable to all observers), then that means you are claiming it is Byzantine fault tolerant with up to 100% of the hashrate faulty. Which obviously violates the fundamental research about what is theoretically plausible. Which thus proves to you that your claim is incorrect.
Bitcoin is the Power Law of Economics, not Byzantine fault tolerance.
Apply that logic to any of the attempts to solve the BGP, you will find that none of them solve it, which suggests that your definition is incorrect. Each and every attempt at solving the BGP defines bounds on the failure tolerance; beyond these bounds, all bets are off.
As smooth said, since the system has failed once it passes the tolerance, how can
it possibly detect anything? That defies logic.