As far as I know, Pride was fully shoot, but all of the companies (and early UFC, I'm sure,) suffered from diving because of gambling and mafia ties. I guess you could consider that worked in a way. Early Pancrase was supposedly lightly worked, but it was set up by pro wrestlers as legit contests in Catch Wrestling, and pretty quickly went straight MMA. I haven't seen any intentional dives in Karate Combat, but I haven't kept a close eye on it. I'd imagine Bas Rutten would weed that out pretty quickly, though.
As far as in-game, the products don't (in my mind) match up with a product like Pancrase, Pride, K1, Karate Combat, etc, because the vast majority of the in-game products leave a huge amount of the match rating up to the popularity of the workers. If you have an unknown sweep into UFC or Bellator, or any tournament fighting format, they can make a name for themselves in one fight. On the other hand, if you have a super popular fighter come into a promotion and utterly stink up the place, they'll get booed back to where they came from. CM Punk comes to mind.
As it sits, 35% of the match rating for Catch Wrestling and Wrestling as a Sport, are raw popularity. Shoot Style and Faux MMA are 40%. It's still 25% for Pseudo Sport at best, but that still feels like it's a very long way from an ideal balance for those products. Faux MMA in particular should probably be closer to 15 (or less, ideally), since a good match is a good match, even if you have no idea who's in the cage, and popularity goes out the window once the first horn sounds.
Edit for clarity.