Replying to myself, now narcissistic...
> Molten salt reactors in general can't cause a meltdown because they are designed to passively moderate in the event of a problem.
At least one design I've seen has a plug in the main salt loop that is made of lead or something with a relatively low melting point. It is actively cooled to keep it solid. If there is a total power failure, and nothing is running, the cooling system shuts off, the plug melts, and the main loop drains out into a containment pool.
The MSR is just running at atmospheric pressure, not super-high pressure like a pressurized water reactor (hence the name). You can crack a pipe, and that's bad, but then the loop will drain out to the containment pool below the reactor. [1]
Unlike a PWR, where cracking a pipe may well lead to a steam explosion. Even if initially contained, this is super bad.
It is unfortunate that many of the reactor designs out there in operation now are not 100% passively safe. Having one or two backup systems (like a Fukushima Daiichi) sometimes just isn't enough.
[1] Now note that recovering from such an emergency reactor shutdown on a MSR is no fun process, and will take a while to do cleanup and get things back up and running. A normal shutdown will not drain into the pool, as I understand it. (Edit: this is wrong, see reply.)