BS”D
While the cause and effect for talking and tragedy is difficult to deal with, I believe the source for the fallacy is that in Middle Eastern synagogues much of the davening is done out loud (as it is in the Moroccan synagogue I davened at years ago) and talking while davening is therefore not as possible as it is in our Ashkenazi shuls.
The rest of it may well be urban legend and not even a verifiable statement from a godol of any note. I do not know what the minhag was in Salonika but that kehilla kedosha was just about totally wiped out in the churban.