The existence of rfi suppression capacitors in some equipment provided a convenient path for current through the rfi capacitor at this higher frequency. The resultant current was greater at the higher frequency. In addition to that, some GFCI models were more sensitive at the higher frequency(yes I measured frequency response = some tripped at less than 1 ma at the higher frequency). The guy down the road at Square D was quite delighted to be informed of that!
Now the point here is different models have different trigger characteristics, so that can explain some of the conflicting experiences.
I am assuming(guessing) the power supply for the pp has a small capacitor connected between each power conductor(black, white) and the grounding conductor(green). When connected to 230V the capacitors currents flow through both in an equal but opposing polarity. When connected to 115V, the capacitor connected to the hot(black) conductor does not have an opposing current from the neutral(white) connected conductor, and that current flows through the grounding conductor(green). Bingo! Leakage current that the GFCI is designed to detect!
Now what about the risks involved if one uses a non-GFCI protected source for the pp. As long as the pp and the circuit are properly grounded, the primary safety protection function is 'alive and working'. The purpose of the grounding conductor is to protect an operator from any leakage(or fault) current by providing a lower resistance path for that current(lower than through the operators body). The GFCI are (partially) a secondary backup protection(in case the grounding conductor gets broke[or circumvented]).
Now the GFCI protection scheme has the added advantage of being independent of external influences(such as broken grounding wires or 2-3 wire adapters).
So IMHO connect to a non-GFCI outlet and be diligent in making sure
the grounding conductors are always functional.
Best scenario is however a grounded 230V branch circuit.
