AI isn't always right but in this case it is. Hanging the rod just above the window frame would make the wall feel shorter and you'd lose the vertical stretch, the window would look smaller instead of pretending it's higher.

To make the window look higher, you can also install a roman shade above the window.

^^^^^This is the perfect answer! I would add a roman shade mounted above the window also. It will make the windows look taller + hide that there is no trim around the windows.