You can rest assured that the rest of the sentence doesn't matter. What does, however, matter is that the person in question works both for the medical establishment and the government, so yes, maybe the stress of placing 'both' at the end was intended by the author.
By the way, the book in question is Educated by Tara Westover.
And here's the complete sentence typed out:
Mary taught nursing at the school, which Dad said was just about as brainwashed as a person could get, to be working for the Medical Establishment and the Government both.