The theory is based on a line from the Game of Thrones book series by Viserys Targaren. He says, “We are untroubled by the pestilences that afflicted common men,” seemingly referring to how greyscale spread through Old Valyria. The Targaryens are descended from Valyrians, hinting they may be immune to greyscale. Other royal characters in the series, including Princess Shireen Baratheon, caught greyscale and survived, but it’s implied that only the Targaryens may be fully immune.

Source: https://www.distractify.com/p/house-of-the-dragon-daemon-targaryen-greyscale