The phrase, "X's depiction of Batman was not true to the original" cannot be parsed as a meaningful statement unless characters do/can have such a life of their own.
I, of course, was trained in a school of thought that took the exact opposite stance from the one you describe. A school of thought that held that role-playing was the highest good, and the interests of the players had no grounds to justify overruling their characterization.
My personal opinion? If you sacrifice *either*, you've already lost. If the only way forward that matches the interests of the players is to depict Vader¹ as a snuggly kitten lover, who funds charities and gives stickers to children, then you should stop moving forward.
¹ real Vader, not spoof Vader, not a dream, not an alternate reality, not…