Bill Zebub
“It’s probably Matt Mercer’s fault.”
It's explicitly Extraordinary and nonmagical in 3e. Explicitly nonmagical.
To me that's effectively the same thing. Arthur C. Clarke and all that. The point being that (in 5e) the ability is explicitly described as imposing the Afraid condition. That makes it an explicit exception to the rule that players decide what they think.
This is in contrast to, for example, the Dragon rolling Charisma (Intimidate) and telling the player, "You now have the Afraid condition." Which in my opinion is NOT ok.