I maintain both camps are correct depending of what you are flying and how you fly it...
No aircraft (that has mass) can change ground track instantly as that would imply instant acceleration.
So it seems obvious that a sudden yaw into wind differs from a sudden yaw downwind. In both cases the aircraft will continue on the original track for a few seconds until the aircraft responds to the new forces on it, the track changes and it either accelerates or decelerates to regain it's original air speed. During that time the airflow over the aircraft is different.
It's equally obvious that this effect dissapears if you make your turns co-ordinated and slow enough that the aircraft has plenty of time to accelerate or decelerate and maintain air speed.
Inertia is very real. Consider a glider decending through strong wind shear on approach. One camp will say the changing head wind doesn't matter because the aircraft will accelerate or decelerate to maintain a constant air speed. The other camp will tell you that due to inertia a glider can't accelerate fast enough to do that and can suffer a loss of airspeed. I'm in the latter camp.