Oh, wow, @WhiteStumbler. I hadn't caught that...
I wonder if that means that prior to Elia and her children being killed by Gregor, the Cleganes were just lowly (if enormous) soldiers in the service of the Lannisters... but that atrocity caused Tywin to raise them up to the level of a House after the Rebellion. If that's the case, no wonder Oberyn doesn't seem to buy Tywin's protestations that he didn't give the order.
EDIT: Even Aemon seems to think it was especially enraging/over-the-top, during his scene with Jon in S1. Maybe there was even a quid pro quo between one of the Cleganes and Tywin... we'll take on this especially unsavory job for you, but only if you raise us up to nobility. I could see Tywin paying his debt in that way...