I'm American, and in American English, we would say "don't they." We would never use "haven't they" when "have" is the main verb. We would only use "haven't they" when "have" is the auxiliary (pres. perf.) As far as British English, I've always thought that both options were used. Now, if the sentence were phrased with "got" ("Everybody has got..."), then I would indeed use the tag "haven't they," because "have" would be the auxiliary verb. But even in this last case, most American English speakers would still use "don't," even if it's technically incorrect.

I believe in American English, "don't they" would be the preferred answer. In some varieties of English, they would, indeed, use "have." Compare: In the United States: Tom has a car, doesn't he? In some other English-speaking countries: Tom has a car, hasn't he?

Afie: I am having difficulty understanding anything at all presented in the question. (A) I do not know what the phrase "question tag" means (B) I could discuss "naturalistic intelligence" in the context of Scientific Data, but you have not shown that your source is a Scietific source. It does matter who writes the claim, because not all persons are clear on the meaning of "naturalistic" or "intelligence". (C) I can understand the use of "Don't they" as an answer, but there is a difficulty here, because although I can understand your answer and accept it as an answer with a slightly sarcastic "edge," your instructor or teacher demands an absolute grammatical perfection. That would be a problem for you and for me, because few Americans as Native Speakers would quibble over the difference. Perhaps relevant also is the fact that your instructor employs a CONTRACTION in a written context. Contractions are appropriate to speech, but arguably, not to writing as text, and especially not appropriate to academic writing. So we can complain about your instructors correction, but our complaint probably will not be heard. Petty criticisms like "haven't they?" occur in academia. .