You're not wrong, but the big difference is who the oligarchs answer to. For instance most big French news outlet belong to various rich people, but they're all somewhat independent and are not watchdogs for the authorities. That might still cause significant conflicts of interest but it's not directly on the government's leash.

Meanwhile if you look at, say, the Echo of Moscow, a popular Russian radio, the main shareholder is Gazprom, the natural gaz company that's state-owned and has extremely close ties with the political power.

That's always the problem with this "whataboutism", it's true that there are many problems with western democracy and freedom of information but it's dishonest to say that it's the same thing. It's really not. I've been learning Russian for a few years and I read (slowly) quite a lot of Russian news and it's really unlike anything I've seen in France or the USA for instance.

Your quotation is missing the most important half of the sentence.

Let's not pretend it did. Media in US, UK and Western Europe aren't controlled by single entity. What is happening in Hungaria right now is basically getting back to socialist one-party regime, even if this time it's right-wing one (like it matters).