I don't know what book that director read but it certainly wasn't Peter Pan. Again here is how Tiger Lily and her tribe are described. It really couldn't be clearer that they are supposed to be Native Americans and decidedly not white.
On the trail of the pirates, stealing noiselessly down the war-path, which is not visible to inexperienced eyes, come the redskins, every one of them with his eyes peeled. They carry tomahawks and knives, and their naked bodies gleam with paint and oil. Strung around them are scalps, of boys as well as of pirates, for these are the Piccaninny tribe, and not to be confused with the softer-hearted Delawares or the Hurons. In the van, on all fours, is Great Big Little Panther, a brave of so many scalps that in his present position they somewhat impede his progress. Bringing up the rear, the place of greatest danger, comes Tiger Lily, proudly erect, a princess in her own right. She is the most beautiful of dusky Dianas [Diana = goddess of the woods] and the belle of the Piccaninnies, coquettish [flirting], cold and amorous [loving] by turns; there is not a brave who would not have the wayward thing to wife, but she staves off the altar with a hatchet. Observe how they pass over fallen twigs without making the slightest noise. The only sound to be heard is their somewhat heavy breathing. The fact is that they are all a little fat just now after the heavy gorging, but in time they will work this off. For the moment, however, it constitutes their chief danger
One important result of the brush [with the pirates] on the lagoon was that it made the redskins their friends. Peter had saved Tiger Lily from a dreadful fate, and now there was nothing she and her braves would not do for him. All night they sat above, keeping watch over the home under the ground and awaiting the big attack by the pirates which obviously could not be much longer delayed. Even by day they hung about, smoking the pipe of peace, and looking almost as if they wanted tit-bits to eat.
They called Peter the Great White Father, prostrating themselves [lying down] before him; and he liked this tremendously, so that it was not really good for him.
“The great white father,” he would say to them in a very lordly manner, as they grovelled at his feet, “is glad to see the Piccaninny warriors protecting his wigwam from the pirates.”
“Me Tiger Lily,” that lovely creature would reply. “Peter Pan save me, me his velly nice friend. Me no let pirates hurt him.”
She was far too pretty to cringe in this way, but Peter thought it his due, and he would answer condescendingly, “It is good. Peter Pan has spoken.”
Around the brave Tiger Lily were a dozen of her stoutest warriors, and they suddenly saw the perfidious pirates bearing down upon them. Fell from their eyes then the film through which they had looked at victory. No more would they torture at the stake. For them the happy hunting-grounds was now. They knew it; but as their father's sons they acquitted themselves. Even then they had time to gather in a phalanx [dense formation] that would have been hard to break had they risen quickly, but this they were forbidden to do by the traditions of their race. It is written that the noble savage must never express surprise in the presence of the white. Thus terrible as the sudden appearance of the pirates must have been to them, they remained stationary for a moment, not a muscle moving; as if the foe had come by invitation. Then, indeed, the tradition gallantly upheld, they seized their weapons, and the air was torn with the war-cry; but it was now too late.