You're perfectly correct that MSRs don't actually run on Thorium. That's one of the reasons they'd be an effective nuclear waste burner.
The advantage that MSRs have over pellet/pebble/rod-based reactors is that when you throttle down, an excess of xenon-135 builds up. This is a neutron poison and damps down the reaction, making it hard to throttle up again until it's decayed (that takes a while. The Half-life is 9.2 hours). Attempting to push through the xenon poisoning by setting the power to 11 can be catastrophic - this is what took out Chernobyl. http://hyperphysics.phy-astr.g...
Because the fuel is not sealed into capsules in a MSR, the Xenon can be extracted into the thermal expansion headspace just before the circulation pump by sparging it (https://en.wikipedia.org/wiki/Sparging_(chemistry)). You need to do this to get helium and other gasses out anyway so it's not a big deal. The end result is that throttling is fully linear and because MSRs don't suffer from steam voids if you snap to full power, the reaction rate can track load at least as fast as a hydro plant and probably as fast as a OCGT plant.
I was going to write a lot more but given this is about space applications it's probably irrelevant. You'll need a thorium blankie for your U233 MSR reactor or you'll run out of fuel eventually. Having it soak up stray neutrons is a good thing in what would probably be a relatively confined space.