They are not wrong, but also not right in all scenarios. Truth very much depends on the reactor design. Thorium is often associated with Gen4 reactors which are responsible for the claims of superior safety. Not much, but some of the safety benefit comes from thorium. Similar for the claim of less waste: Some reactors have better neutron economy, burning their own waste down to more shortlived and therefore "better" isotopes. Or, by the same mechanism, can utilize existing waste as fuel. Also, continuous loading and separation of isotopes only works well with liquid fuels which is a Gen4 idea.

Thorium is more of a side-topic there.

On the economic side of whether thorium is cheaper, the submission argues in a very underhanded manner. Yes, fuel is cheap compared to building the plant in all cases. But the fuel cost of thorium is an order of magnitude below uranium due to no enrichment (for light water reactors in the fuel, for heavy water reactors of the water). And possibly (for liquid core reactors) the unnecessary fuel elements production.