The real story is that what you hear on the video was almost the basic track to the song, but not quite. The film company, doing what film people do ("Don't worry, you won't even know we're here"), put everyone on edge, causing Paul McCartney and George H. to get into a row (which is why George is in the control room instead of playing). The next day the band took what they thought was the basic track to Trident Studios because it was the only studio in London that had an 8 track tape machine at the time, and the band wanted the extra tracks for the various overdubs to come. It seems that they had a difficult time transferring what they did at Abbey Road to 8 track, so they wound up recutting "Hey Jude" again and then finishing it at Trident.
There's a lot more to the story, including how the song had to be saved at the last minute due to a giant problem, but you'll have to wait until Ken's memoirs are published. The book is titled Abbey Road To Ziggy Stardust and will be available for preorder soon (publish date is June 6th). In the meantime, you can read a lot more about the book by going to the Abbey Road To Ziggy Stardust website.
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