There’s another aspect you have to consider: the power dynamic. If MSNBC hired Jen Psaki or Fox News hired Hope Hicks because she got sick of working in government, they might have a bias towards their former colleagues but it would be voluntary and clearly a job either would be qualified for. That’s pretty different from, say, Russian government going to RT and giving them a list of qualified candidates or even, say, the Tories appointing their loyalists to the BBC because the decision isn’t being made by the government and there isn’t a threat explicit or implicit that there would be consequences for not hiring them.
Another power dynamic to consider is that MSNBC or FOX have owners (Comcast and Murdoch respectively) and those owners have shareholders (Blackrock, Fidelity etc.) who also have holdings in corporations that get their revenue from government contracts (Lockheed etc.) and so MSNBC executives feel pressure to hire employees who will generally take a positive view on the delivery of large government contracts to corporations, government-structured tax breaks and bailouts for corporations, and so on, and of course a government employee with an eye on possibly returning to a government career is an acceptable option, because they will promote the opinion that this is a great system that doesn't need say, more audits or investigation into misappropriation of public funds and so on.
Now the word for this kind of integration of the corporate world and the government world is....?
"Fascism should more properly be called corporatism because it is the merger of state and corporate power." — Benito Mussolini
