Mercenaries have been a part of warfare since people have had currency to hire extra fighters, and back in the iron age, it wasn't uncommon for massive portions of any army to be made up of mercenaries. None of that is really anything new; it's just that it's becoming trendy to start paying attention to it. You name a war and large groups of mercenaries are present.

I'm pretty much working on a darkly comedic and over-the-top RP that has the premise that nations are second to massive corporations and mercenaries are pretty much the most viable occupation in the world, so it's not like it's the most unheard of idea that people are worried that PMC groups are going to become more powerful than nations, but good luck finding one that's going to try to try to take over a country without being paid to do it. They're a business, first and foremost. It's a lot easier and cheaper to focus on fighting a war on behalf of a country and let them deal with the logistics of governance and the PR game. They only make money if somebody is fronting the bill, which is exactly why PMC groups can afford all the top of the line hardware that your average soldier can't dream of obtaining. If one decided that they wanted to overthrow and rule a country, even if they did somehow out-battle and defeat that country's military (not really an easy feat, considering that the only countries worth taking over probably have more funding and military power than the PMCs will ever hope to have, and there's a very real threat of that country's government freezing that PMCs assets and screwing them financially), then they have to deal with the threat of a civil uprising and inherit all the problems that that country faces just running the damn thing, and as soon as people find out that there's a rogue PMC group, good luck to them ever trying to get work again.

They have nothing to gain and everything to lose if they, according the end of the video, "Decide to stop taking orders."

Oh, and then there's things like they probably wouldn't be able to leave whatever country's airspace that hired them because if they did have air assets, they'd be intercepted, and if they tried to take an airport out, they'd probably have their passports revoked. Really, it's nothing more than a fun fictional idea with no practical weight behind it. Once again, their success and wealth depends entirely on nations bankrolling them. They'd never do something so stupid as to lose that support. 

And if for whatever reason they were hired by another country to attack another country, than that's still country A declaring war on country B, so nothing changes that way.