They don't own The Pokémon Company, at least not in its entirety. Nintendo isn't even a majority owner.
The Pokémon Company is also owned by Game Freak, Niantic, Shogakukan, Takara-Tomy, Banpresto, and a bunch of other companies that handle different aspects of the Pokémon franchise. (Formerly Creatures as well, which was the biggest owner. I believe with Creatures gone, now it's Takara-Tomy.) Because they are a Japanese production committee, they are all owners in the same sense that Nintendo is an owner. Decisions can't move forward without approvals from enough of these parties because they are ALL owners. They are basically a larger scale version of a board of directors. There is a chairperson, but even they can have their decisions overruled if enough of the other representatives say no. That is, there is no one in The Pokémon Company whose decisions are absolute.
This is why Pokémon does its own thing separate from anything else associated with Nintendo (such as Pokémon Directs mostly running separately from Nintendo Directs). It's not completely a Nintendo property. Nintendo actually has to get approval from the other parties in The Pokémon Company for Pokémon characters to appear in a Super Smash Bros. game.
Nintendo is trying to gain more control in an indirect way. The other parties have voted to kick Creatures out of the committee in light of the bad press the franchise had received in 2019, undoubtedly because they know Creatures is responsible for it in some way. Now, if this is true, Nintendo wants Game Freak closer to more easily give them support and advice where they need it.
Most major Japanese media franchises are run in this way, for the record. Dragon Ball, for instance, has partial ownership by Shueisha (publisher of the manga), Toei (studio behind the anime), Bird Studio (Akira Toriyama's brand), Namco-Bandai (publisher of most the video games), FUNimation (English anime localizer), Viz (English manga localizer), Banpresto (primary merchandiser), Figma (secondary merchandiser), and other companies that receive and give away ownership according to what happens at the corporate level with the franchise. Any major decisions have to go through all of them first, though they don't necessarily have to get unanimous approval first. This is why, when you look at credits for major release anime, like Attack on Titan or JoJo's Bizarre Adventure, you'll often see "(name of anime) Company" or "(name of anime) Committee" as a creator. That's the collective name for the production committee.