Mesae, you make perfect sense. Another way to look at this in an intuitive way is as follows: You are in a 100kt airspeed glider in no wind conditions. Therefore ground speed and airspeed are the same. You commence a 180 degree turn at 3 degrees a second, and in one minute are heading opposite the way you came. Your ground speed went from 100 one way, to 100 the opposite way. Net change is 200 knots in one minute.

Now, same situation, but flying into a 100 knot headwind. Ground speed is zero. You are motionless over the ground. You now commence a downwind turn at 3 degrees a second, as before. One minute later you are on the reciprocal heading. What was the change in ground speed? Simple, it was zero one way, and a minute later 200 the other way. Net change in one minute is exactly what it was in the no wind situation. 200 knots. Same change in speed relative to the earth in the same time frame.

When you are airborne, there is no wind. Don't believe me? Go up in a hot air balloon in a howling gale, and tell me if your hair will be ruffled.