Chosing words carefully, let me say that the experiences described below were settling, and they did have power, but they were not VRS (or settling with power) aerodynamically, at least not to start with.
The classic downwind turn is a killer because the aircraft is slowed through zero knots and then accelerated backwards. This drives the rotor through the peak power point, where there could very well be a big power shortfall. The aircraft starts dropping, the pilot pulls what power he has, the bottom falls out and he calls it settling with power.
VRS or settling with power requires that you descent to eat your downwash, so the descent speed must already be there to start the VRS. The situations described start from a mild descent, and with the big changes in power required due to the downwind condition, the descent begins because of a power deficit (This is NOT settling with power, as confusing as the words are).