I like to defer to a particular scene in Episode 5 for this matter. Specifically, when Dlanor thanks Battler in the rose garden for the duel they had earlier on. Battler remarks that that was not him, just the piece version of him that Lambdadelta wrote, but Dlanor responds that pieces specialize in actions appropriate to their original personality, therefore it was certainly something Battler himself was capable of.
I think since the game boards / tales themselves are acknowledged as fragments on the meta plane, it’s not off the mark to assume the characters are accurate representations of their real counterparts. Saying “it isn’t real” isn’t getting us anywhere fast.