There are quite a few of these stories that are false, actually.
The infamous "Donkey Kong 64 had a bug that nobody knew how to fix, but the Expansion Pack randomly fixed it, so last minute they decided to ship the game with the pack" was also debunked by one of the main developers. Apparently the game did have a killer bug near final production, which required some crazy last minute work to fix, but nothing related to the Expansion Pack and they were designing it with the Pack from the very beginning, as Nintendo wanted a title to show it off.