Now that you mention it, I do remember the story of Blythe's death. His portrayal in the book and series is most likely fairly accurate based on the testimony of those that served with him. It was these same men who were responsible for his "death". None of them knew what happened to him, he was severely wounded and they thought he died which is what Ambrose wrote. As the HBO series was based on the book, it also has him dying of his wounds. It wasn't until after the series came out that his family became aware of the inaccuracy and corrected it. So later editions of the book have the correct information but the early editions and the series do not.
He did go back into the army after the war and died on active service in 1967.