I agree that the aircraft does not know what the air in which it is flying is doing, to a point. I have been taught that at the slow side of the aircraft speed scale, where wind speed is faster, inertia can begin to play a role in pilot perception, and then performance.
Flying helicopters in the offshore world it was not uncommon to have 60 knots of wind when taking off from a platform. Climb speed in our particular aircraft was 75 knots and the turn to downwind while holding climb speed was visually spectacular if not seen previously.
Though I have nowhere near Megan's experience flying helicopters, during my training, the balling out I received turning downwind after takeoff was memorable. In the SW300, I was climbing nicely after translation, and with lots of room under me (though not established in the normal [airplane] circuit yet), I gently turned crosswind then downwind. My instructor lit into me for that, explaining that the inertia of the helicopter might be overcome by the change in apparent wind direction relative to its mass, and would not accelerate fast enough with the wind to maintain the IAS and the rate of increase of groundspeed, and re-enter translation He went on to demonstrate the effect of allowing the helicopter to be caught by and apparent (to the helicopter) increase in tailwind, and begin to settle as more power had to be added to maintain the climb. It was a memorable demonstration. He is a 20,000 hour helicopter pilot, so I listened to what he said.
I accept that the effect is probably minimal to none with an airplane flying a normal circuit or at normal speeds, as it does simply move with the air. My experience with STOL equipped Cessna floatplanes has been that it is possible to get into an alarming situation turning downwind during a low speed climb, when trying to evade rising terrain. I agree that gusts, terrain effects, and increasing windspeed with altitude would be factors in the perception of decreasing performance. If the pilot could climb ahead safely, they probably would have. If they have chosen a low speed climbing turn, terrain is probably a factor in their decision. then they are flying with visual reference to that terrain, and may try to fly more slowly than they should in the climbing turn. Though a steady wind may not be affecting performance singularly, the combination of effects of wind and perception can get a pilot in trouble. I have experienced this in low powered skiplanes and floatplanes, where tight climbing turns in confined areas resulted in the sensation (or stall warning) of degraded climb performance at that speed. I've known two pilots who have reported to me after the accident that as they climbed in a turn, the wind caught them from behind, and they settled into the trees. In both situations, my senses allowed me to believe that they experienced a combination of terrain effect, and increasing windspeed as they climbed - but they still crashed in a downwind turn, where a climb ahead would have worked fine.
When dissected in physics, I'm sure there are purist answers which differ. From my training and experience, I fly and train others that this is a cautionary, or avoid if possible situation.