The problem with stories like this is that this kind of story is what makes it to the front pages, whereas stories about how well a plant operates or its lack of incidents is never even put out to the public. It is like that old adage "One oops wipes out a hundred 'atta boys"
A lot of the older population still remembers the first TMI and Chernobyl. That is all they know about nuclear power. Unless you worked in the industry or the Navy, lived near a plant, or had family in either of the first two groups, you knew nothing about nuclear power except for the disaster stories. The only exception is when people hear about the need to build new reactors, and then people STILL think of those two blemishes. They don't understand how nuclear power works, and they don't want to take the time to learn. Now if someone was to make a video game about it that somehow involved space aliens, we might get through to the next generation. It is an our unfunded job to educate people about nuclear power and to dispell several of the myths about it. However, as Marssism has pointed out, "Don't argue with idiots", so there will always be those who think that the "China Syndrome" is the gospel and that we are just out to cover it up with our propaganda and to make money.
Until we start seeing people actually take the time to research how nuclear power really works(even if it is wikipedia), we will always be dealing with the negative perception of the public based on those two incidents. Most people if they have a bad day at work, they end up burning someone's hamburger, losing a major contract, or crashing the company car. There is a little pain, but in the end it is pretty easy to get over. If nuclear power has a Really bad day, that part of the Earth is unihabitable for many decades. IT is hard for people to get past that, unless we explain to them how much we learned from those two incidents and why this is a very small chance of it happening again.