The challenge with nuclear energy is we don't have a big enough sample to say with certainty, just from the data, what the odds are of a disaster 1000x worse than Chernobyl.
My understanding is Chernobyl itself could have been 1000x worse and rendered much of Eastern Europe uninhabitable if the appropriate steps weren't taken in time, so to a neutral, non-expert observer, that would seem to indicate the odds are greater than zero.
This is what many anti-nuclear people are concerned about, so if you want to get them on your side, you need to explain in detail why that kind of event is no longer possible. Just stating that it hasn't happened, as if that were proof it can't happen, isn't convincing.