Bob Denver and Alan Hale

I know that with movies like these, the script writers stay true to life on some things, and embellish other things to make the film more interesting. What I would like to know is if there's anyone who knows if the film's portrayal of Bob Denver and Alan Hale meeting for the first time was real or embellished. It was one of my favorite parts of the movie. Alan had just arrived on set for his screen test and he had been introduced to Bob, and Sherwood Schwartz was telling him that what the show really needed for the Skipper and Gilligan was chemistry between the actors. And before he could even finish talking, Bob suddenly ran up to Alan and yelled, "SKIPPER!" and then he jumped into his arms. And after catching him, Alan just smiled and said, "Well hey, little buddy!" I thought that it was just the cutest thing ever, and if anyone else knows, I'd like to know if that was really what happened when they met. I'd like to think that it was, but you never know with movies.