I think you'll find that Doc 31 hasn't been updated since FTE and OAA got their MPL approvals.
The information did not come from Doc 31 but from a PLD employee who flies at our club.
It matters not whether you believe it, a simple call to the CAA before signing up for the course will confirm the truth or otherwise of the allegation. A small price to pay, I would have thought. Alternatively, you could ask for sight of OAA's approval certificate.