What you say is technically true but you're forgetting decay heat. The fission chain reaction stops if you remove the moderator in any sane LWR design, but the fission products in the fuel will continue to generate a very large amount of heat for quite a while. This is exactly what happened at Fukushima and TMI.
Some reactor designs can dissipate this decay heat with passive circulation, while most require active pumps to circulate for a while after shutdown. But a total loss of coolant is probably going to result in fuel melt to some extent.
Which is equally a problem for a molten salt cooled reactor. If molten salt leaks or pumping stops, you're gonna get a melt down in your molten salt reactor. That is unless it's running at super low power density - like these guys: https://www.usnc.com/mmr/, in which case no cooling fluid or pumps or even natural circulation apparently are needed to keep it from melting.
MSRs have an advantage though, which is that a) fuel melt is obviously not a problem and b) if something goes out of control you can pull the drain plug and drain the entire core into multiple crit-safe storage pools. Dividing the core up makes it easier to handle the decay heat, though I'm not sure exactly what any of the current designs do in detail. Fission product gasses are also not soluble in most of the fuels for MSRs which makes it easy to filter them out, which reduces the decay heat to an extent and also mitigates the reactivity feedback effect from xenon that caused the Chernobyl disaster.
Not that it's all sunshine and roses, hot salts are awfully corrosive and that's been the primary engineering challenge on every MSR design I'm aware of.
Yeah. Decay heat is still an issue but MSRs are inherently able to handle it without the need for active circulation. Plus if shit hits the fan like I said you can drain it out just with gravity into a configuration that is inherently unable to continue fissioning without the need for reactivity control. So, no need for active circulation pumps nor a reliance on the ability to ram in control rods... plus you don't have to worry about hydrogen buildup either.
The idea with molten salt reactors is that they aren't under pressure. Unlike a PWR, which will experience more and more pressure until it pops, a molten salt reactor can handle much higher temperatures before failing. This enables designs that can be passively cooled in the event of coolant system failures.
https://en.wikipedia.org/wiki/Decay_heat#Power_reactors_in_s...
Some reactor designs can dissipate this decay heat with passive circulation, while most require active pumps to circulate for a while after shutdown. But a total loss of coolant is probably going to result in fuel melt to some extent.