A lot of stuff that is theoretically guaranteed to be a disaster looks very safe and profitable until shortly before disaster strikes.
Nuclear plants can, in a worst case scanario, be given the SCRAM treatment to shut them down hard. If that procedure is successful then the reactor is off.
The worst case is probably like Chernobyl but involving multiple reactors. The probability of that is pretty low not only because Chernobyl served as a wake-up call, but because what happened at Chernobyl was an unfortunate chain of events that focused on only one reactor.
So in the worst case secnario you have a disaster which creates a new national park-sized area you can't live in. Compared with coal plants which used to render large portions of the continent unlivable for the hottest, haziest, smoggiest days in the summer, that's an acceptable risk.
It isn't as simple as that, with a lot of reactors. The ones at Fukushima were SCRAMmed. A running nuclear reactor will build up a collection of fission products that have various half-lives that can cause problems. In Fukushima's case, these fission products continued to decay and produced lots of heat (about 6.5% of the heat produced during normal operation, according to https://en.wikipedia.org/wiki/Fukushima_Daiichi_nuclear_disa...). It was this heat that raised the temperature of the fuel and boiled off the cooling water and caused the disaster.
So basically, with lots of reactors, SCRAMming is not enough - you need to maintain cooling for quite a long time afterwards. It is entirely possible to build reactors where this is not the case.
An appropriate response to the turkey statement along these lines is to ask where the farm is and what people it serves. There are many farms in the world where statistically, Thanksgiving makes no difference to the mortality of the Turkeys.
Accounting for Murphy's law, and that the worst case is always x% below your expectation (even after accounting for Murphy's law).
