Except in the FAQ it is clarified that "the wearer is not a actually wizard" which is why they can wear armour. However not being a wizard stops them from casting spells.
And this means
nothing according to the rules. It's a piece of flavourtext and you're making your own interpretation about it instead of just taking it for what it is, a piece of flavour text. This is literally the "discarding broken lances"-FBIGO bit from the first FAQ again. You're trying to interpret a rule that doesn't exist, so you're making up your own rule and overthinking it.
What does mean something according to the rules, are the actual rules for the Wizarding Hat, and they are extremely clear: The wearer is a Level 1 Wizard, with all that entails. The FAQ just clarifies that the Ogre Tyrant wearing it isn't an actual wizard (the power comes from the Hat) and can still wear his armour - but he still follows all the rules for a Level 1 Wizard thanks to said Hat. Nothing in the FAQ changes this.
Thats all there is to the FAQ, it's just a clarification that the Wizarding Hat doesn't prevent the wearer from using armour. Nothing more.
Answer me this, can a character with a Wizarding Hat:
- Cast spells? If yes, what bonuses does he have and why?
- Dispell spells? Regardless of "Yes" or "No", why Yes or No?
- Miscast? And if so, what happens?
... I guess I am standing on this hill after all.