Earlier in the season Isaac said he was 63 years old, which means he would been around 14 in 1951 when the game in question took place, making it very unlikely he would be covering the game as a member of the press.
When Dan is talking about the 1951 Dodgers - Giants game he says it was a one game playoff. While a one game playoff for two tied teams is the practice since 1969, the famous Dodgers-Giants playoff was a three game series. This is done on purpose. Real-life events require permission to use, any real,people involved in the event can complain, or sue. It's always done like this unless they have direct permission.