The possessory credit is a contract term

The phrase arrives on screen looking like a statement of fact. It is not. It is a contractual entitlement, negotiated individually, granted to some directors and withheld from others, and the Writers Guild has spent decades objecting to it on precisely those grounds.

Knowing this does not settle any argument about who authored a given film. What it does is remove one piece of apparent evidence from the table. When the credit appears, it tells you about someone's representation and leverage. It does not tell you who made the thing.