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Targaryens are not immune to diseases. During Great Spring Sickness in Dunk and Game of Thrones Tyrion Lannister happy father’s day shirt of Targaryen family died. So, not catching Greyscale is in no way indication Tyrion is Targaryen. Maybe Tyrion just got lucky. Any character who makes it through more than two books is this world must be heavily protected by plot armor. Otherwise we would not have even one protagonist who survives long enough so we could develop any emotions for him or her. This would hardly be a compelling story if there were no characters for us to get invested in throughout all the books, if the protagonists all were exchanged after ten chapters.
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So: plot armor for the main characters is needed, be they Tyrion, Dany, Game of Thrones Tyrion Lannister happy father’s day shirt or whoever. Plot armor or hanging around in some remote boring place off screen. So if Greyscale was meant to bring down the Valyrians (hence being referred to as Garins Curse) then the argument that Tyrion is a Targ coz he hasn’t caught it is redundant. Essos is full of people of Valyrian descent. Shireen Baratheon has Valyrian blood. We do not have much data, but I cannot recall that the Great Spring Sickness affected Dorne. I really do not know if Jon Connington has any Valyrian blood, but I’d say that only the Rhoynar are immune to greyscale.