as to whether this one (i forget the name) is privately owned, i have no idea.
That house is called Falling Water.
Growing up in Connecticut, one of our neighbors was Anne Baxter, the actress, who’s grandfather was Wright.
She had a house that looked very much like a Wright, but it wasn’t.
This one is called FallingWater, and is owned by the Western Pennsylvania Conservancy. It is open for tours and private functions. The stream (w/the freeze thaw cycle of W. PA) has done some damage to the structure, and the Conservancy, thru funds generated by the tours, etc., maintains the property. It is trully stunning. It was built by the Kaufmann family (they owned a major Pittsburgh department store chain) and I believe bequeathed to the Conservancy.
......i’ve always wanted a house with a stream that runs through it. ;) .....
The Falling Waters house is no longer possible because it is built in a Flood Plain.
FEMA prohibits and most counties support the prohabition of residences within the 50 year flood plain.
I lived across from one. Subsequent owner paid many thousands re-routing the stream and stabilizing the foundation. And that was before he had to re-roof and re-side the place.