Just watch the Blithe episode. That was something Ambrose got wrong and corrected in later editions of the book the series was based on.
Blithe didn't die a few years after the war. He was discharged in '45, lived and worked in Philly, then reenlisted in '49, and serving in Korea where he received a Bronze Star and Silver Star, Taiwan, and Germany. He was still in the army when he fell ill at a ceremony in Bastogne and died after an operation for a perforated ulcer in '67.
None of that takes away what was an outstanding book and series.