I think it might actually be the other way around, because Ash only had access to regular Pokeballs, and red had all kinds like ultra, master, great, etc. And when Ash fought gym leaders, they had unevolved versions of the Pokemon that they had in Red's era, like Sabrina's Kadabra in Ash's time and it's Alakazam in Red's time, and Erika's Gloom and Weepinbell both evolved. The Cinnabar Gym is destroyed then relocated just like in the anime, and, speaking of gyms, due to Ash not defeating Giovanni, the Earth Gym was still around, so Red had to fight him, and due to Ash not defeating him, Team Rocket was still very active in Kanto. They look almost the same too. Blaine is still a bald dude with glasses, and Giovanni is a businessman in a suit, Lt. Surge, a tall man in military clothing. Also: think about the Pokemon Center. In Red's time, it takes mere seconds to heal a Pokemon instead of waiting for hours on end for your freaking Pikachu to get some rest. Also, Gary looks shockingly similar (at least in Season 1) to Blue Oak, carries the same last name, and both had a grandfather in the Pokemon business. It's very possible that the Professor Oak we know and love in Pokemon Red, Blue, and Yellow is actually Gary.
GARY MOTHER****ING OAK.