It's not really. There is millions visibly spent on lobbying efforts against climate change, and invisibly stockholders invested in energy are board members of media companies. For example Jack Cockwell has over a billion dollars in Brookfield hedge fund, and that fund has been increasing it's holdings in energy for the last decade. There's some BCE board member that has millions of dollars in Wajax stocks (industrial equipment manufacturer), about half his net worth.
If you talk about industries with influence on one another from the perspective of ownership, you'll find it's all very incestuous as the richest people will diversify.
Weirdly, the people involved in Fox News only seem to own stock in FOX, but cash contributions to those people aren't shown in the market data I'm looking at. Maybe I'm not looking in the right places, but I'm not a finance person.