The only explanation I can think of would be, maybe it would be considered such a high offence to impersonate the emperor, that most people wouldn't even consider it possible?
The announcer on the radio would have said who was going to speak. Yes, the penalty for impersonating the emperor was death, so no one is going to do it. The emperor spoke at that time in a very odd, archaic, hyper-polite speech that virtually no one had ever heard or used before, so a large percentage of people listening to the emperor's speech couldn't understand him, anyway, though they could tell that this was a special, imperial form of speech.