1) I am not saying other countries didn't have their own version of Vaults. Vaults weren't the the only reason people survived the Great War. I would say Vaults only saved a very small fraction of those that survived. But Vault Tek didn't build Vaults outside of America. American tec would not be found outside of the USA. Robots, Laser weapons, Power Armour and such wouldn't be outside of America.
2) America didn't have people stationed overseas at the time of the Great War. America became extreme isolationists and closed its borders.
1) every company that existed before 2052-55 can have an office wherever in the world and the company's that was building vaults is far older then that. Robots, Laser weapons, Power Armour and such was used by US army wherever in the world they operated!
And no one have still put any proof that Robots, Laser weapons, Power Armour and such was not made in the rest off the world! But we know China china was working on PA, that china and Europe was making energy weapon and we have faced chinese made robots!
2) America had most certainly people stationed overseas before 2055 and at least some of those base's must have stayed in US control. and even at around 2060 when US was fully isolated nothing prevent them from operate on foren ground !
And when they entered the war whit china they def start to operate on foren ground!