I've always seen this theory as a very transparent attempt to forge Tyrion some +5 plot armor by connecting him to the shadowy prophecy thereby necessitating keeping him alive.

By the numbers though, this only works if somehow Tywin didn't know. Which is unlikely given that the only good relationship he ever had was with his wife. And he likely knew exactly how long he spent apart from her making a clandestine affair rather difficult. Because if he knew Tyrion would have been long dead before coming to Winterfell. And that add more to an already fairly unlikely tale.

And Tyrion is so like his father. While Targaryens in particular seem to run a crap-shoot between bat-**** crazy and decent guys. Tyrion is neither.