Nice call out. Never considered this aspect of secrecy but I can kind of see it but would also be interested in possible reasonings.

A secret can be seen as hidden state so if as a person, you have no hidden state then perhaps in an operational sense, you're replaceable. There is plenty of hidden state however that isn't classified as a secret. Say you know a system better than anyone else. That knowledge may not be secret so much as inconvenient for others to obtain. Maybe that disproves the statement since non-secrets can still distinguish.