It's important to remember that the ultra-powerful and wealthy live whatever life they want to live regardless of what their media companies promote.
Someone can own a media company, have it push very specific political ideologies with the goal of turning people against each other and gaining power for themselves. By pushing antagonistic media, they can prop up fringe political figures who'd be more willing to help them with their political goals. (E.g. tax policies that help the wealthy person's companies.)
They can still live whatever life they want, even going against the ideologies the media companies espouse, because they're rich enough that the fallout doesn't impact them.
They're living a very different kind of life than us.
BTW, I'm not explicitly arguing that Larry Ellison is doing this -- I don't have the context or background on that. I am saying that his media companies will 1. do things to help Larry's interests (which are probably political), and 2. that doesn't have to be aligned with however he lives his personal life, since he's effectively immune.