I believe yes, a bettor has the right to refuse if he don't want to expose himself publicly because it is also for his own safety. Who would want to be broadcast for winning huge amount? Your relatives, friends and everyone will become aware that you became lucky. You'll be at risk as being a target of bad people.

But I think it depends on the country where you from and their rules when it comes to this kind of event. Here, if a gambler win huge in lottery, it is announced publicly but the winner remain anonymous. Obviously it is for the sake of the winner and to avoid any inconvenience.