The only way to reliably get around this is to have a separate, non-partisan funding mechanism for news. For all it's flaws, it's why the BBC tends to do well. Just being independent isn't enough (see The Independent as an example for that).
Side note, this is partly why the BBC gets a lot of flack for both sides - when they say things that support one position, the other side invariably accuses them of bias. Even they don't get it right all the time though, and never will (being run by humans who, you know, get things wrong).
The best thing America could do for it's political system is outlaw media outlets from reporting news and being for-profit. Instead, set up a slush fund of a few billion to pay for all news, and then ban themselves from interfering except to punish those who are partisan one way or the other.
Reporting should be about educating people as to the state of the world, and local, relevant information. Not entertainment.
Fun fact: in the UK, this trend really started with the publishing of the memoirs of Christine Keeler in the News of the World, which also kicked off the rise of Rupert Murdoch's empire. The scandal that ensued became known as the Profumo affair and by location centred around Cliveden House, which has 400 acres of woodland which include the cottage where I live.