The reality is:
* Al Jolson's voice was used extensively throughout the film.
* Larry Parks did sing in the film, but his voice was limited to a few songs and spoken dialogue.
* The studio, Columbia Pictures, was not unhappy with the results and considered it a success.
The rumor likely arose from the fact that Parks had a singing voice that wasn't as strong as Jolson's, and some viewers may have noticed a slight difference in vocal quality between different scenes. However, this was intentionally done by the filmmakers to show the evolution of Jolson's voice.
In conclusion:
* Al Jolson's voice was the primary vocal source for the film.
* Larry Parks did sing a few songs, but his voice was not entirely replaced.
* There was no need for a "vocal impersonator" like Walter Craig or Grant.
The myth of a studio replacing Jolson's voice with someone else is just that - a myth.