This stops being true for quick changes - because there's still the inertia of the aircraft. So if the wind speed changes quickly, the aircraft can't immediately move along with it.
This is why gusts are so dangerous to landing aircraft. A strong gust from behind can cost you all your lift, and a strong gust from the front can temporarily stall your wing.
A tail wind is just saying that the air is moving in a certain direction with respect to the ground (the same direction the plane is flying). The plane doesn't give a shit about that.
Fortunately that kind of instantaneous change doesn't happen in real life.
Jet stream boundary is usually not this sharp, and the airplane would fly much faster than the difference anyway.
You can feel a much stronger pressure in the sail when moving towards the wind on a fast windsurfer/windfoil as you can do 15-20kts 45deg towards the wind, giving you an apparent wind that is 10-14kts stronger than the true wind.
On the same craft, going away/downwind, you will feel the apparent wind at a similar angle 10-14kts less. In fact, because of the change in drag and forces, you'll probably be going faster and feel even less wind on the downwind leg.
When you turn, this can be a big benefit for going downwind (jibing) as at some point the sail feels zero apparent wind (your motion cancelling out the true wind), feels very light in your hand, and easy to rotate to face the other way. Even knowing the physics of it, the timing and execution is still something that takes a lot of practice...especially on big race gear with a 9.0m2 sail.
Lift only comes from the interaction of the air and the wing, so if there's zero relative motion then you will fall out of the sky, regardless of if you have a 200 knot groundspeed.
This also means that, if the wind at altitude is above your plane's stall speed, you can hover in place by flying straight into the wind! (example here: https://www.youtube.com/watch?v=n_e6ijREScE)
Similarly, if you are in a packet of air that is moving at 200 knots, the fact that you are moving at 500 knots indicated airspeed does not mean you are flying supersonic from an aerodynamic perspective, despite having a groundspeed of 700 knots.
The only connection a plane has to the universe is the air around it. It simply does not know or care what the ground is doing until the ground is quite close.
A small plane in a very high wind is perfectly happy having a "backward" ground track.
Same thing as if you were trying to swim upstream in a fast river. How fast you move through the water doesn't have anything to do with how fast the water is moving across the land.