I'm not sure, I didn't understand it either. If they were going to have someone else do the voices they should have put Curly instead of Curly Joe.
I found out that Joe Besser actually did voice a character on the show.
Besser kind of had a late career resurgence as a voice actor. In THE NEW SCOOBY DOO MOVIES, he voiced Babu in “Mystery in Persia” (as that was a crossover with the JEANNIE cartoon series). I also personally believe he voiced the villain at the end of “The Weird Winds of Winona”, but have never found a source for it (it doesn’t help that Hanna-Barbera at the time was not crediting voice actors with what roles they played).
After rereading that quote in THE THREE STOOGES SCRAPBOOK, it seems that Larry implied that the Stooges weren’t allowed to voice their characters, which makes no sense to me. They clearly had to allow their likenesses to be used for the episodes, so couldn’t they have made it a stipulation that they had to voice the characters?