Very interesting situation. Haven't come across this myself, but it sounds more like 'chance' than anything. What I've found, after a little internet research, is that hair dryer cords might be GFCIs, but there also might be one-time-use immersion protection or a cut-down (two wire) version of a GFCI called an ALCI. Here's a quote from the Conair site:
Conair? manufactures its hairdryers with two different kinds of safety plugs. The ALCI is known as an Appliance Leakage Current Interrupter. This unit has the "Reset" button and the "Test" button. The circuit is looking for leakage of current between the two conductors. This unit sometimes trips when lights are turned on and off, when the dryer is plugged in, or when a new dryer is taken out of the box and plugged in by the consumer who doesn?t know how to operate the RESET feature. An IDCI refers to Immersion Detector Current Interrupter. This unit trips only when the dryer has been immersed in water. The dryer should never be used again after immersion because of the potential dangers a water-damaged unit presents to consumers. That is why this unit trips once and is not resettable -- because it shouldn?t be used again!
Very little information about ALCIs on the web. But, basically, it is 'like' a commercial GFCI with current transformers and a comparator. Unlike a typical GFCI, the ground is connected only to the applicance and not the electrical EGC. They are apparently prone to nuisance trips. Snapping on clippers makes perfect sense, with capacitance in the raceway and both circuits next to each other at the panel. I suppose you could try another circuit, to test the things to see 'how' sensitive it is. Don't know whether these things wear out, but it would be interesting to call the hair dryer manufacturer to see what they have to say. ("We went to ALCIs because people either buy new dryers or cut them off so we have no product liability" sound likely?)