I can recall two or three occasions when people have approached my aircraft when I've been sat on the ground, engine running. One was potentially quite dangerous as the chap had a dog with him (not on a lead).
On each occasion my response was to yell a warning to keep clear. I honestly can't recall thinking about shutting the mags off, although with the blessed hindsight that this incident has given I rather think I will consider it in future.
I've discussed this with a few aviating friends, who, like me, fly from isolated rural strips. We all agreed that shutting the engine down was one of the last things we would instinctively do. One raised the point that, as his engine took a long time to warm the oil, he'd be quite focussed on waiting for the temperature gauge to come up before taxying, and may not be as aware as he should be of his surroundings (like the accident aircraft his engine is a Rotax 912S, that is quite slow to warm up in cold weather).
As for the view that this chap was "chased" by the gyro, all I can say is that the limited manoeuvrability, restricted steering accuracy and limited stability makes this challenging for the gyro to do. I would imagine it steers on the ground rather like a flexwing microlight, which has the ground handling capability of a child's soapbox cart.
VP