I firmly believe that they don't hate each other. It took me some time to study Jin's relationship with people to be able to actually write Akame or just him. I realized that no matter how many people say that there's a rivalry scene between them I can't really see it. With Yamapi I can see that he's got this competitive streak in it - best example was him joking about how he failed the Nobuta audition and Yamapi got it instead in Cartoon Kat-Tun 100. Jin's one who's not above making jokes about people in their faces (like how he joked about Ueda possibly wanting him to quit Kat-Tun in Oshareism), but he didn't say "I failed the audition that's why Kame's in it". In Music Station when they were in he called Yamapi "cheapskate" (but had been consistently mentioning about how idol-like Kame is), in a show where both him and Yamapi were doing solo numbers.

The strangest thing about them is how they were never shown to be estranged, but the media seem to like the idea of him hating Kat-Tun, hating Kame and everybody. Making him out like he's the selfish rebel whose only intention left is to hog the glory by himself forever.

By media concluding did you mean the interview that Black Mayonnaise did?