We can easily see how the media is influenced by big business. How can we see it? By the many people who have been de-platformed, and by the numbers of articles and videos being censored.
What could the media do if they were honest, but simply didn't like the opinion of somebody? They could simply set up one or more sections in their systems, where they could place what they considered to be junk news or fake news.
They could even make rating system algorithms that sorted items into a bunch of categories, depending on how fake or junk they thought it was. Nobody would have to be censored or de-platformed.
So, we can see from this that most of the major media companies don't fairly control the material they show.
You make a really intriguing argument concerning the nature of "news" itself. It is true that what constitutes "news" is always changing, and various individuals have different perspectives about what is noteworthy. When it comes to news, it appears that the distinction between subjectivity and are at odds. On the one hand, we want news that is impartial and factual. On the other hand, we want the news to be compelling and informative. It's a difficult balance to achieve. Additionally, algorithms are employed to select what news is presented to us on social media and other channels. However, algorithms might be prejudiced, reinforcing our pre-existing views and preferences. This may make it tough to develop a system that's honest and consistent.