You ask for empirical evidence that "private entities have the inability to create money out of thin air", but this rests on a definition of "money". You brought up the example of a private IOU (the Poker Site).

If we remove the distinction between private IOUs and bank IOUs, indeed you would have an example of a private entity creating money out of thin air, for a more loose definition of money. However, as we established, removing this distinction is unwarranted, bank IOUs are treated quite differently both legally and materially.

If we maintain the distinction between private IOUs and bank IOUs, then your example becomes simply irrelevant. Any IOUs that may be issued by private entities that are materially and legally different from bank IOUs have no bearing on Werner's claims.

I believe the empirical evidence for private non-bank entities not being able to create bank IOUs is that they're not banks. Am I missing something?