I thought Keith had disliked Perez for a long time.
Ages ago, Keith tried to stop him acting like a dick and realised it was a waste of time.
He also disappeared quick smart when Perez was doing his endless pathetic silly act in front of him and KP, saying something like 'rather you than me' to KP.
He hadn't been overtly horrible to Perez, but that doesn't mean he liked him at all.
When he got voted out, Keith was jubilant, relieved isn't even the word. Perez must have driven him crazy, and when he got out, he admitted he really had no time for him.
He is a patient man and he tried, but in the end he just realy disliked Perez who was horrible.
Nothing mysterious about any of it, no 'plots' needed.