That is completely bizarre - not only is that scene crucial to the story, it's also one of the most memorable scenes in the film. I got a copy of the American VHS (clamshell case, "Walt Disney and You" promo at the end) circa 1984/85, and can say with certainty that the scene was left intact in the USA.
Alternate Versions: Early video releases were missing the magic sequence with the dancing puppets. Disney's response to complaints was that music rights were not available.
Music rights occasionally came into play in the early days of home video, but it was really
rare until the music industry became overtly greedy in the 21st century. What makes it particularly weird is that the song, "Skipping Along," was explicitly recorded for the film. For anyone who's interested (and doesn't wanna shell out the money for the full soundtrack CD), the song is available as an mp3 from an album entitled "The Richard Haymen Collection":http://www.amazon.com/gp/product/B00JRMOBF2/ref=cm_cr_thx_view
I think i have an answer. I was just watching and on the wall are diiferent screens showing various rooms and Tia's pink bedroom is seen. I think the idea of that old man with a camera in a little girls bedroom is the reason for the missing piece