The backup test
A copy of the system will travel. Restorations, support, the ordinary movement of data that every durable product eventually does. The test is simple. After the copy exists, can it be used to impersonate someone? If yes, something that can authenticate was stored as if it were merely a record.
The cheaper decision is to store only what can verify. A value that confirms a claim, without being spendable as that claim, survives a copy. A value that can be replayed as-is does not. We apply that test anywhere a secret or a proof of identity would otherwise sit next to ordinary data.
The rule is not a particular mechanism. It is a placement: anything that can be spent as access does not belong in the record.