How can you make stereotypes "authentic?" That frankly makes no sense. Had there been no mention of this "authenticity" at all, I would not have given the production of "Peter Pan" a thought.
But as I've said before, the whole idea of placing Indians in a fantasy Neverland is problematical. Therefore, I agree with this writer. Replace the Indians with a fictional race--elves or Munchkins or whatever--and the story would work just as well.
For more on the subject, see Tiger Lily in Peter Pan: An Allegory of Anglo-Indian Relations.
Below: A more authentic Tiger Lily from the recent Peter Pan movie.