Splott Man, Yes it's true - acording to the Internet Movie Data base, that Jean Hagan actually used her own voice rather than that of Debbie Reynolds for the movie within a movie, shown in "Singing in the Rain."
As to the idea about the speeding up or slowing down of movie sound tracks. I don't buy it. I still think that the different key thing is a deliberate in joke.
The examples of non-existant guitars and the like are more like slack mistakes. Cheers, Joy