A single entity can simply take control of an enormous share of national media, dictate what kind of coverage is and isn’t acceptable, and shape the public’s understanding of the world according to its own interests. That’s fine, because that entity isn’t the government.
The public could check this in all sorts of ways, from enacting strict rules around the acquisition of media outlets, to wielding anti-monopoly powers to prevent concentration of media ownership, to the creation of more publicly funded, editorially independent news outlets, and maybe even the reinstatement of rules like the Fairness Doctrine. Under free-market dogma, however, the public is only permitted to nod along as corporations “chill free speech and the free flow of ideas.”
Don't forget, it's all about controlling the money to have all the power.
The argument against government interference is an argument against dictatorships, but government can be extremely democratic. Therefore, the corporatists are against democracy if it's too good (if the People control rather than the elite few).