Jon doesn't have purple eyes or light hair either but I'm fully convinced he's a Targaryen.
It's also possible Tywin either didn't know Tyrion wasn't his or because of whatever reason that hasn't yet been revealed he was forced to live with it.
Or it's not true and is just a theory. Who knows.
It's also possible Tyrion is a Targaryen on the show but not in the books.
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