Taking Pictures On Pueblos Prohibited?

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A story on the local news says taking pictures of or in pueblos is prohibited. There’s several pueblos near Albuquerque and the Rail Runner goes through them. The train conductor attempts to stop passengers from taking pictures of the Pueblos while the train runs through their land.

What is their legal right to prohibit photography where it’s legal to photograph in every other public location in the US? Can they really do anything about it? What will the Rail Runner do if someone continues to take pictures?