It's a fact, though it goes aginst most basic flying training guidance.
Essentially, as has been pointed out, the a/c momentum keeps it at the same relative groundspeed, so that a turn downwind results in a loss of airspeed. Conversely, if you stonk along with a strong tailwind and turn into wind, the airspeed will increase. Try it next time you have a chance, it is very clearly seen in any more than about 25 kts of wind with a light a/c (or any helicopter).