Bear with me....If, Tyrion is actually of Targaryen lineage, as is theorized by some, perhaps he is/was immune to the greyscale in the water, much like Dany was immune to the fire in the climax of Season 1.
Or, greyscale can only be contracted by skin to skin contact.
The show seems to possibly be hinting at this. Keep in mind that there was a conversation between Tyrion and Tywin about Tywin not liking but simply dealing with Tyrion due to not being able to prove that he wasn't actually his. The Mad King and Tywin had a good relationship, but in time the mad king grew fearful of Tywins influence and power,
Also, Tywin suddenly turned on The Mad King when it was extremely risky to do so, and keep in mind he DID NOT anticipate Jaime killing the Mad King which sealed the deal. Jaime made that choice on his own. Which was more about saving thousands of innocent people than just saving his dad, as Jaime confessed. Tywin used Roberts rebellion to get control of the Kingdom and take out the Mad King, but again, this was still VERY risky and Tywin is smart enough to know that. This was a move of passion in my opinion on Tywins part. As I believe The Mad King RAPED Joanna Lannister as a swipe towards Tywin.
Tyrion 'killed' his mother during childbirth. But the theory goes that Tywin tried to poison the baby before it was born and hence Tyrion was born a dwarf, and the mother was the one that actually died.
Then also keep in mind that Tywin got REALLY pissed at Tyrion when asked if Tyrion could take control of Casterly Rock. Tywin wasn't necessarily the shallow type, he was in it for the win, and it's always been clear that Tyrion although 'deformed', was probably the most capable of leading, due to his keener intellect compared to Cersei, and having more ambition than Jaime.
Tywin had real disdain for Tyrion, and you can't imagine that it had anything to do with how he looked. Tywins smart enough to know that Tyrion wasn't responsible for his wifes death, so why be so abusive towards him? Again, Tywin himself said he couldn't prove that Tyrion wasn't his, but he said before Tyrion killed him that "you are no son of mine".
Tyrion also was set to death for the false accusation of killing Joffrey, something Tywin used as a reason to kill Tyrion for, though most would agree that Tywin was smart enough to know that Tyrion wasn't the culprit. Tywin now had control of the Kingdom through Tommen, whom hec ould easily manipulate, who also wasn't the moron that Joffrey was. Tyrion at this time wasn't needed anymore, and killing him because he was 'guilty' of killing the King, would help Tywin save face.
Plus these tidbits. Tyrion is drawn towards Dany. Tyrion also made out to be good friends with Jon Snow, the only Stark he actually got along with, and they seemed to have a mutual respect in the 1st season. I don't think those scenes had no reason behind them. Plus, in the books he also dreams of dragons and has visions, similar to how Jon and Dany have.
The only counter to this is the possible emergence of Aegon VI, but this may not happen in the series, as he should have already shown up. So if he doesn't show up, whom else is the third head of the dragon?