I suspect the reality is somewhere between the two positions being taken on inertia.
Consider the example of wind shear. As a glider descends to land it experiences reduced headwinds due to wind shear. According to one camp a glider shouldn't notice this reduction in headwind - it's ground speed should "automatically" increase to maintain a constant airspeed (afterall it's lift drag and weight and trim hasn't changed so it's airspeed shouldn't change). In practice due to it's mass and inertia a glider cannot accelerate fast enough so it does experience a loss of air speed if it descends rapidly through wind shear. Glider pilots typically add half the wind speed to their landing speed to allow for this effect and for other reasons.