The argument is wrong because coal is as bad as nuclear power. Both are limited, both are centralized systems and both have huge environmental impacts. Mining, transport, energy production, and also exhaust and waste.
It should also be noted that coal mining is done the worst conditions you can think of. I'm very glad that by 2018, Germany will stop its coal production completely and not only because it is very expensive to get the coal in Germany.
This is btw something you have with all fossil and nuclear sources. With time it will get more expensive to get to the fuel needed. And according to the German government, nuclear fuel comes only partially from mining. So mining is currently not delivering the fuel for all nuclear power plants running. The rest comes from old nuclear weapons and other sources, according to the German government.
Also it should be noted that nuclear power was never really profitable. It might be with old plants now but with newer plants I think it is unlikely to earn a dime with nuclear power unless you get some kind of subsidy. The new EPR currently being build in Finland already costs 100% more than expected. With that money you could have installed enough windmills to cover those 1600 MW the EPR might provide.
Nuclear power was used for about 50 years, it will leave us with waste for the next 100,000 to 1,000,000 years.