Did that girl have what those stone guys have that touched that one guy who use to be under the queen of dragons? Why hasn't he turned into a stone guy yet?
The girl had it, but was somehow cured because her dad spared no expense in saving her, only to later burn her at the stake.
The guy who used to be under queen of dragons also has it, but it takes time to spread.
In the books, they mention that children often survive grayscale but are left disfigured (I think they even casually mention other children/adults with scars) but that it is always fatal to adults. Think of it like a nasty version of chickenpox.
Also, to grayscale nerd out, its supposed to be an allegory for leprosy. Many substances have placeholder names (milk-of-the-poppy:opioum, dragonglass-obsidian, etc) in the series and some of the descriptions of greyscale are similar to medieval qualities of leprosy (those afflicted are considered "unclean", shunned off to colonies of the infirmed). As such, leprosy is not something just anyone can get. Only people whose body temperature runs on the low side are susceptible to it. Dany having dragon's blood is far too spicy for grayscale. Boom.
