The letter from Sam Oppenheimer, Jr, was a prank
Think about it - why would a big time New York theatre producer go to a tiny town to see a production of a musical about said town? Sam Oppenheimer, Jr, was probably the 13 year old son of Sam Sr who was forced to work in his dad's office over the summer instead of being able to spend time with his friends. While sorting through mail he decides to screw with this random guy and tell him that Mort Guffman is actually coming to his show. When the day of the show actually comes, Sam Jr comes up with the worst excuse possible - a snowstorm in July - to explain why Guffman isn't actually there.
At some point the agency realized what happened - this probably wasn't the only person Sam Jr pulled this prank on - and when Corky contacts Guffman, he genuinely feels bad that he fell for it and tells him he can come audition for his latest production as a way to make up for it.
