I keep wondering how a Rubbia thorium reactor would handle a natural disaster of Fukushima level intensity. As I understand it the nuclear chain reaction would stop instantly if the power is cut, but nasty waste products such as Uranium-233 would still require substantial cooling and hence it would seem that this reactor is just as unsafe as any other type of reactor with definite risk of meltdown, radiation and other problems?
You are focusing on entirely the wrong thing.
A reactor burning Thorium produces fission products (like all reactors), including the majority of the heat source as well as radioactive Iodine and Cesium isotopes. The problem with Fukushima was mostly the release of such isotopes into the atmosphere (ultimately, isn't all of nuclear safety concerned with this?). However much heat U-233 produces is completely beside the point when you ask to compare it to Fukushima, it matters, just not for this question.
The key design feature of the Rubbia proposed reactor is that it is a subcritical accelerator driven reactor. To the extent that it uses a solid fuel form that does not have active fission product removal it is subject to the aforementioned problems.
The problems of sustained removal of decay heat in even the most dire of circumstances, however, have been addressed very well just with the next generation of reactors we are building today (although the concern can never be completely eliminated). The "passive" designs share the same fuel type with Fukushima (and almost all other reactors in the world), and just use natural forces to cool the reactor for weeks to months after an accident so loss of power isn't a concern. These same passive design principles could (and would) be applied to the Rubbia reactor design, because the Rubbia idea addresses concerns very different from the problems at Fukushima, which include sustainability and criticality safety.
The reduced radioactivity of accelerator driven subcritical reactors and Thorium reactors is not the short-lived stuff that creates problems during accidents. Mostly they reduce the long term waste and the unused fuel.
Fukushima incident has reached current scale due to human fails (both at the engineering, construction, operation & disaster mitigation stages), not natural disaster.
No matter how safe is the reactor, if humans will continue to ignore safety for the sake of profit, such fails will continue.
Thorium reactor is indeed 'safer' to a some degree, due to the fact that combined activity of wastes is lower, but If we had Thorium reactor at Fukushima, we might have had similar result (i.e. destruction of all cores & release of comparable(maybe some 2 times less) amount of radioactivity into environment). Yes, cooling is also needed for thorium reactor is shutdown state.
Although, it is possible(and it's being done for modern reactors) to have both thorium & usual uranium reactor built which are able to stay cooled passively for extended period - but still probably not long enough for fukushima case.