Actually, the fan was correct.
She held the Master Sword in Wind Waker, but she never did wield it. She was giving it to Link. Wielding means holding and actually use the weapon.
And if you want to go with specifics (since yes, you did nitpick a bit)
A baton isn't a Master Sword.
A Sword in Spirit Tracks, well, there was no master sword in that game.
All of these, not only makes the question actually valid but also the answer correct.
And who gives a rat's ass on whether he got it or wrong for something that specific?
What Reggie wanted to know is that he didn't confuse Link with Zelda.
A fan is devoted into loving the franchise and knowing at least the very common things about said franchise. That doesn't mean he needs to know every intricate details.
Should I know how many enemies and which types there are at the 42nd floor of the Cave of Ordeals in Twilight Princess? Come on Bruh.
EDIT: FYI, she didn't posssed a Darknut, she possesed a Phantom.
By your definition, for making such a misshap, should you not be a fan?