I'm with I,Brian and Gumboot on this. The idea that Tyrion is the ******* son of Joanna and Aerys never held much weight for me anyway, specifically because there really wasn't much in the way of solid evidence to back it up. Yes, I've read all the clues as to why the theory exists, but I personally don't feel it stands up.
I think Gumboot raises an excellent point as well; it's all but established canon fact that R+L=J. The evidence is overwhelming. But to have that exact same type of situation with another character cheapens the use of such a thing. Part of why R+L=J works is that Jon's parentage has always been in question, Tyrion's, not.
Would we all like to believe that Tyrion's natural father was not the wretched monster he was raised by? Sure, but it's not the case. Let's examine a few things about Twyin's character:
Twyin Lannister is known for his unparalleled intelligence, cunning, and ruthless (we'll exclude Tyrion himself for the sake of argument). There's a reason you can't ask the Reynes of Castamere about how Tywin deals with slights. Yes, Aerys II had kind of a thing for Mrs. Twyin, which caused understandable friction between King and Hand. Twyin isn't the type of man who would "suck it up and deal" with his wife being constantly hit on in front of him. He put the blame with Aerys, but I cannot and will not believe that if Tywin so much as suspected that Aerys had done anything more than ogle his Joanna, he would have found some way of retribution, and for a slight that personal, he would not have remained quiet/idle waiting for the perfect opportunity with the uncertain prospect of war. A personal slight requires personal retribution. With Tywin being as exceedingly intelligent/cunning/ruthless as he is, he would've taken more immediate action.
As to his comments that Tyrion is not his son, that's simple. Tywin Lannister is a great and powerful man. Aerys II's paranoia and jealousy drove Tywin to quit as Hand, and Ser Ilyn Payne lost his tongue for saying that it was Tywin Lannister to truly rules as king. Tywin is an epically formidable foe; feared by lords and smallfolk alike, even those warring against him tread cautiously, and the lords of the realm know that to stand against Lord Tywin Lannister means you're tossing the dice because if you lose, you lose everything.
A man as great/powerful/feared as Tywin Lannister knows damn well his reputation precedes him, and it's a reputation he relishes. A man as infamous as Tywin Lannister hides nothing and is ashamed of nothing. Except... there's no possible way I could have fathered a dwarf. That mangled, stunned, grotesque little thing did not come from my loins. No possible way. We Lannisters are lions, chiseled out of alabaster, emeralds and spun gold. That little creature isn't mine.
But if that's the case, why not just kill Tyrion? It's flat out stated in the book that if Tyrion were "not a Lannister," he would've been slaughtered or left out to die of exposure the way the small folk handle "grotesques." If Tywin had serious cause to believe that Tyrion were not his own, two things would have happened. 1) Tywin the ruthless would damn will have gotten rid of any get not his own, especially a deformed one, and one that killed his lady wife. 2) Tywin the ruthless would have gone after the man who raped his beloved lady wife with all the cruelty, cunning, malice and rage he had, determined to destroy every last thing the rapist held dear.
Again, this is a personal thing. One could argue that Tywin did take revenge on Aerys II (presumed rapist) by destroying the Royal Family. But technically, Tywin didn't. Tywin quit as Hand and went back to Casterly Rock. He sat around while Robert warred his way through the realm, and showed up in KL once Robert's victory was all but assured. Not only did he not personally kill Aerys, he had no hand in it at all. It was Jaime's action, not based on anything his father said/did/etc., but based on saving lives. As for Elia and Rhaenys, sure he ordered them to die, but they certainly weren't involved in Joanna's 'rape,' so I view that as an entirely separate issue.
Tyrion, much to his chagrin (and secret shame), is Tywin's son.
