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Some Targaryens are fireproof (e.g., Dany), some people can’t seem to be able to get the hang of staying dead no matter how much they’re literally killed (e.g. Beric Dondarrion, Lady Stoneheart, wights, if you consider them people, Ser Robert Strong)… plenty of the supernatural going on in those books.
Dany isn’t categorically fire-proof in the books. She survived a one time special event, with the help of the ululating chant and some kind of magic. But after that, she could be hurt by fire.