Exactly so, but each company (nintendo, game freak, creatures) has their own set of rights to various pokemon names, and the pokemon company kind of coordinates and manages them. As I understand it, they're more facilitators and ensuring all things pokemon are handled with one voice. I feel like I should learn more about how this kind of business model operates X'D
Nintendo, creatures, and gamefreak have equal ownership of the pokemon franchise and pokemon company, they created it to manage the worldwide merchandise since between gen 1 and 2 it had become a worldwide phenomemon of massive scale. (it seems very recently creatures sold its third of the ownership but i can't verity this.)
the initial partnership happened because Pokemon gen 1 initially was not a nintendo game, but a GF standalone as GF is a fully detatched third party; however, they ran out of money and went to pitch the concept to nintendo who helped in exchange of getting of ownership and they also made creatures do the same thing, either to spread the risk investment or because they needed more money. If GF had the crystal ball and knew pokemon would be so successful, they most likely would never have done this deal and would have gotten funding somewhere else.
Nintendo doesn't own gamefreak in any capacity, however nintendo owns the copyright of the pokemon name, such as the franchise title, pikachu, the characters, etc. gamefreak can and has made games on non-nintendo platforms, but i imagine it's mostly wasted effort since they have what prints gold already so they keep it to a minimum.
to complicate things further, nintendo owns a part of creatures. nintendo also fully owns the pokemon trademark, so i imagine this means that a pokemon product can only ultimately be allowed by nintendo's decision (GO, those old pc tutorial card games, etc). I think if this weren't the case, you'd see mainline pokemon on every platform and it'd sell 30million copies+ per title, especially smartphones nowadays.
tl;dr
the franchise ownership part means all 3 companies have equal weight on business directions regarding the whole franchise (development investments, merchandise distribution, creation of cards, touraments, marketing, cartoon, movies production, design direction/production of the new pokemon, salaries etc, including the decision to outsource any of it - as it recently happened with a few recent pokemon designs that have been commissioned to popular artists outside of the company) - the trademark part, which is fully owned by nintendo, means nintendo has the final word to what official product goes where. this means that the company does not fully operate in nintendo's best interest, just a third, but nintendo has a leash on where the products go.
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