I've been resisting this one, but my strength ran out... actually I think both sides are right, subject to the appropriate context.
Of course the aircraft does have inertia relative to the ground. So if the wind changes instanteously, there will be a change in IAS for the time it takes the (new) force of the wind to effect an acceleration. It would take more tedious math than I can be bothered with to work out how long it would take, but based on what it's like hovering or doing pedal turns in a gusty wind, I'd say not long - a second or two max.
In a steady wind and a normal banked turn (heli or fixed), the time it takes to change direction is significantly greater than this wind acceleration time, so it has no noticeable effect. Otoh the visual effect of the changing ground speed can be very striking, especially at lower speeds typical of a heli. The first time I flew a heli in the pattern with a 30 knot wind at 1000', I found it very noticeable and it took a conscious effort to focus on the airspeed indicator and not the ground. (Much less of an issue in even a small plane at 80 knots than in a heli at 60). That is what (so they say) causes problems for low-time fixed wing pilots - they see the ground suddenly rushing by and they reduce power or pull on the yoke, and stall.
Gusts are a different matter. A sudden gust or wind-shear can turn 60 knots into nothing in a fraction of a second. Airliners have fallen out of the sky because of this on several occasions (higher absolute speeds of course, but 727s don't hover very well anyway) - although their extra mass and much smaller ratio of effective frontal area to mass probably makes it a lot worse for them than an R22 or a 152.
If you were OGE at 1000' and had a sudden 60 knot wind change (i.e. 30 knots N turns to 30 knots S), I guess you'd feel it but you'd have time to add collective and unless you were watching the altimeter like a hawk it probably wouldn't be big shock. Same thing at 30 feet or 3 feet and it could indeed spoil your whole day. (I confess I didn't read the G-TIGH report so I don't know what their altitiude was).
My 2c, off to bed now...
n5296s