The only time I ever personally encountered 'nuisance' tripping was on a commercial food processor in a co-op where I would cook. This was a small beast that used a 1/2 hp induction motor in its base (rather than the more common brush universal motors). It would trip the GFCI receptacle every 3 or 4 starts....then one day just after I'd pureed some soup and cleaned the machine up, it simply turned itself on and smoke started coming out of the base. It turns out that the waterproof boot on the main switch had cracked, and enough liquid had gotten in to short past the switch. To this day I don't know if it was in fact nuisance tripping, or leakage around the switch.
Regarding inductive loads and current balance: If you think of an ideal inductor isolated in free space, there is no way that more current could flow out on one leg than return on the other leg. But in this case the inductor is _not_ isolated in free space, and is not ideal. In particular there is capacitive coupling to ground all around the circuit. I would expect _some_ imbalance current caused by this capacitive coupling, since the two terminals of the GFCI are now part of several pretty complex circuits.
However I suspect a different issue. A GFCI is supposed to trip on current imbalance. However what a GFCI really does is measure the current induced in the secondary of a current transformer with all of the conductors being tested fed through the aperture. If the conductors don't equally couple to the transformer (leakage flux through the air rather than through the core), then even with perfect current balance, there will be some residual current measured detected by the transformer. I suspect that the inrush current to many inductive, or the starting current for many motors could create a total balanced current that is high enough to cause an false imbalance reading.
-Jon
