I think that is what we've effecttvely been told - something about the switch or the low voltage caused 'the MCB to overheat'. Note that the thermal trip in an MCB is a heater, and the NSH is a heater, and they're in series. So if the MCB is correctly rated, if it overheats, the NSH element will too (maybe not enough to notice or cause damage).
I think I'm with DW on transferred heat so far, although all 4 MCBs would have had to be pretty darn close to the edge.
But I do like things to obey the laws of physics (even if the wife doesn't!). Troubleshooting electronics often takes one along many steps from cause to effect, e.g. bad backplane connection caused data errors, caused incorrect parameters loaded into drive, caused overspeed, caused limit overrun, caused output bridge overcurrent, caused transistor failure, caused heavier overcurrent, caused PCB ground track failure, caused driver bypass capacitor to explode. Tortuous, but each step is a logical consequence of the last.
Here, it feels like a non-sequitur. e.g. Bad connection caused smokes to get wet caused giraffes to get restless caused capacitor to explode.
E2A Marconi - DP main sw does not normally have leading neutral contact (only TP+N). PF of heater will be very close to unity, unless it has some fancy PWM drive or something spurious - was one of my earlier q's.