The classic wire sizing assumes that current from the three phases
will cancel into the neutral. When the current is dominated by higher
harmonics, namely big current spikes at the peak of each sine wave,
they add up; they don't cancel because they are not simultaneous in
time.
While I very much doubt that the harmonics will actually burn down the
house, the (possibly urban legends) that the harmonics have burned the
neutral conductor in a cable, causing hazardous voltages appears to be
believable.
At higher distribution levels, it is assumed that the neutral current
will cancel out in a three phase system and thus, the neutral
connector might quite a lot weaker than the phase connector. In a
ground cable, the armoring around the phase conductors might act as
the neutral conductor. In a pole mounted cable system, three aluminum
phase connectors plus a steel cable servicing as the mechanical
strength as well as the neutral condition (assuming neutral conductor
canceling out).
However, if this canceling assumption is not true with electronics
load, the third harmonic current is far larger than initially assumed,
causing burn through of weak neutral conductors.