It started off as a joke. Somebody on the internet combined the initials of Teams Galactic, Rocket, Aqua, Magma and Plasma to get GRAMP. In the games, the Generation I rival refers to Professor Oak, his grandfather, as "gramps." By putting two and two together, one can draw the conclusion that Professor Oak is the secret mastermind behind every major villainous team in the Pokémon franchise.
While this "theory" was likely never meant to be taken seriously, it can be expanded upon. In June 2016, a YouTuber posted a video that put some real thought and research into the lore of Pokémon to show how the theory could hold water. According to his research, Professor Oak has the potential to be one of the most powerful men in all of Pokémon.
One of the things that makes Oak so powerful is his far-reaching influence, starting with various items gifted to the player. Through the Pokédex, Oak knows everything about the Pokémon that trainers encounter, battle, capture and evolved. The Pokégear and Xtransceiver let Oak keep track of not only a trainer's contact information but also their precise location. If the Pokémon Storage System works as it does in the anime, then it also gives Oak free access to any Pokémon not being used by a trainer. The combination of all the technology a trainer has access to gives Oak everything he needs to know about that trainer, including their status and progress.
He also knows the most about Pokémon in general thanks to his large network of professors. Oak personally researches the relationships between people and Pokémon. Professor Elm, Oak's student, has done research on Pokémon eggs and evolution. Professor Birch studies Pokémon habitats and environments. Professor Rowan knows even more about Pokémon evolution. Professor Juniper looks into the origins of Pokémon. If all this information gets sent back to Oak, that would make him the ultimate information broker of all things Pokémon, which could theoretically make him unbeatable in a battle.
Oak also has the potential to hold influence over some powerful trainers. His connections to the professors, for example, give him access to the people they are most familiar with. Professor Birch has connections to Gym Leader Norman and their children Brendan and May. Professor Rowan has a connection to Champion Cynthia as the one who gave the girl her first Pokémon. If Oak played his cards right, he could get both the professors and their associates to do whatever he wanted.
Oak himself has also made some powerful connections directly. His own grandson is a Champion-level Pokémon trainer. He's also apparently got history with Agatha of the Elite Four. This is to say nothing of the countless trainers who have received Pokédexes thanks to him. Not only does Oak have the potential to ask favors of these people, but they're likely to oblige due to their trust in him.
As for how Oak can possibly win over the hearts of so many people, he has his charisma to thank for that. His role in the story should be proof of this. He's one of the first faces a player sees and helps them when they're just starting out. He even provides them with their starter Pokémon. From the moment he meets someone, he can earn their trust with his helpfulness and generosity.
Even if he can't get the player to do what he wants the nice way, he can always get what he wants through blackmail. Again, Oak has access to the information of several new trainers, including their location and even their experiences. He could easily find and exploit the weaknesses of any of these trainers should they choose to stand against him directly.
This would probably be a good time to bring up how the villainous teams tie into all of this. The theorist doesn't go into depth about how these teams all came to be under Oak's thumb; it could have been through charisma, blackmail or something else. However, what's interesting about his theory is the true purpose of these teams.
While it seems like all of these teams fail miserably, this is just another part of Oak's plan. However important it is for these teams to achieve their individual goals, the player standing in their way makes for a calculated loss on Oak's part. These relatively minor victories are meant to distract the player from Oak's efforts to achieve his true goal: world domination.
If the theory that Oak is a grand puppet master ever somehow turned out to be true, one would need to look no further than where Oak has ingrained his tendrils. His potential influence can be felt throughout the world of Pokémon. If he wanted to, he could definitely take over the world.