That being said, in these cases media and politicians tend to align over time, either because media help compatible politicians, or because politicians created the media landscape themselves. Oligarchies tend to be symbiotic. For those close to power, anyway; for the rest of the country it’s more like parasitism.
https://en.m.wikipedia.org/wiki/Manufacturing_Consent
IIRC Noam Chomsky and Edward Herman make the argument in "Manufacturing Consent" that basically consent can be manufactured in the U.S. because of the role that business and corporations play. Which is sort of a critique of capitalism, but I also recall Chomsky talking about how it's hard to really call the U.S. capitalist considering how much of the military industrial complex and academia (especially defense-related) is government funded, and how central those things are to the U.S. econonmy.
I'm not sure of the details but my takeaway is media consent can be manufactured in a corporatist/capitalist-like system, which may also be but is not necessarily an oligarchical one.
I think that concentration of wealth in the hands of an ever-shrinking elite is a form of oligarchy.
Also the whole idea of a government / multinational divide gets a bit blurry, doesn't it, when you look at the longstanding U.S. government relationship with companies like G.E. , A&T, etc, and, I'm sure in one form or another, today with Google and Amazon.
I mean government-funded research created the tech giants.
Lastly, as much as people love to knock government, ideally it's how people organize to do stuff, and, has an accountability mechanism (elections).
I'm kind of riffing off of what you are saying but yeah. Power comes in many forms and can be abused in many forms.