Ah it is all explained with a dose of Bullshittonium.
While I could actually believe that satellites survived the great war Bethesda writers don't seem to realize that the BOS was never about spreading their... well ideals around and have other people form chapters in the rest of the country, and why should people in West Virginia decide to form a chapter of an organization whose members they have never met in person? (Bethesda "Welll because Maxson was very charismatic before the war and had many followers." Me "Bethesda, Maxson was a regular military officer in the army, he wasn't fucking Big Boss."
The BOS is about survival of their own members and maintaining their level of technology, hoping one day to outlive the rest of humanity and claim Earth for themselves.
They even stopped recruiting people several decades before the Vault Dweller came, mostly likely because they saw outsiders as inferior and did not want their technological secrets to fall into the hands of wastelanders.
You don't fix your mistakes by retconning lore.
What next if you have to explain the BOS presence in a region where they should not be. Well teleportation exists so you probably resort to that but lets also had time travel to that one; the BOS has a time machine. (why they don't use it to prevent the war in the first place is everyone's guess, or use it to secure useful materials and people right before the war)
Or long range mind control; the BOS controls the minds of wastelanders in another state and make them for another chapter of the organization.
