Actually, I've seen plenty deep dive lore videos on the Fallout games. I haven't seen the show but Vaultec starting the war in consistent with the lore. If I recall one of the most damning bits right, there's a Vaulttec logo on the bomb in megaton. There's also hints that the Enclave was also involved and it was a larger part of a space colonization effort for the elite, see Nuka World expansion for that.