"C Kingsbury" wrote
The number in the book is for a plane at gross weight with the engine at
idle. It's the number at which the rudder runs out of effectiveness to keep
the nose aligned with the runway.

Actually, no. It would make sense if that were the case, which is why
it's not

In reality, the max demonstrated crosswind component is at least 20%
of Vso - and above and beyond that, it's a compromise between what
legal and marketing want. It's certainly not the best the factory
test pilot can do, and depending on technique it need not be the best
you can do, but there is no guarantee that the max demonstrated
crosswind component will not be more (or less) than the plane can
handle by the wing-low method at short field approach speed. It's not
a certification requirement.

BTW, lightly loaded makes crosswind harder, not easier, because your
stall speed goes down, and thus the crosswind as a fraction of stall
speed goes up.

Michael