Is a Rubbia thorium reactor safer than other modern reactor types? 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?
 A: 
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

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.

I keep wondering how a Rubbia thorium reactor would handle a natural disaster of Fukushima level intensity. 

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.
A: 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 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 in 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 the Fukushima case. 
A: The question of cooling was addressed exactly to Carlo Rubbia after his presentation at the international thorium energy conference (iThEC) 2013 hosted at CERN.
He pointed out that, in case of a sudden total shutdown, the proposed design (CERN-AT-95-44 ET http://cds.cern.ch/record/289551) can be substantially air cooled with channels that surrounds the reactor, just taking advantage of convection, without forced ventilation. This should guarantee the safety as long as the air intakes stay clear.
Another important point is that not only the U-233 keeps heating the reactor after the accelerator goes down, but also its concentration keeps going up being produced by slow beta- decay of Pa-233 (produced from Th-232 by neutron capture). So if you want to be really safe you need to operate your reactor quite below the criticality. This imposes very strong requirements to the intensity and the reliability (up-time) of the accelerator complex which, related to its cost and efficiency, are still far from being solved.
