Solti's statue as a pianist is well-known. He occasionally teamed up with the likes of Ashkenazy and Perahia. There are quite some conductors who are accomplished pianists, even apart from pianists-turned-conductor. Tilson Thomas, Pappano, and many more I can't think of right now.
I don't believe Solti would have interfered with Larrocha's playing. As if she needed that, and he was too professional for that. But I think he could be quite a fierce creature. Probably had a row with Alicia about some interpretative detail. I bet the ever-sweet Alicia could also show her teeth if needed. Neither of them were real Mozart specialists and perhaps wanted different things. Ah well, nice to speculate on something like this