In this sentence

People have been telling themselves the story of Snow White for centuries.

Is themselves reflexive or intensive. I am thinking intensive because you do not need it for the sentence to make sense?

That word should either be immediately after "People" (therefore intensive) or should be removed. It is not needed in this sentence.

No, it's reflexive. Without "themselves," the reader would assume that people have told others this story. In addition, "themselves" in this sentence is an indirect object and does not emphasize the subject.

http://www.mcwdn.org/grammar/prorevlexin.html

In the sentence, "People have been telling themselves the story of Snow White for centuries," the word "themselves" is used as a reflexive pronoun.

To identify whether a pronoun is reflexive or intensive, you can follow these steps:

1. Determine the subject of the sentence. In this case, the subject is "People."
2. Identify the pronoun that follows the verb. Here, it is "themselves."
3. Ask yourself whether the pronoun reflects back to the subject or intensifies the subject.

In this sentence, "themselves" reflects back to the subject "People." It means that the people who have been telling the story of Snow White are also the ones receiving the action of the verb. Without the reflexive pronoun "themselves," the sentence would lack clarity about who the story is being told by.

Therefore, the correct interpretation is that "themselves" is reflexive, as it is necessary for the sentence to convey the intended meaning.