OK well we can add that to the simple explanation. If the top airflow is diverted down when it wants to go straight, it would still want to go straight therefore pulling the top surface up, right?.
So it's more complicated than that.
Downwash (in the context of lift generating wings) refers to the downwards motions of air generated by tip vortices (look-up "induced drag" for more details). This is not the same as the net downwards motion of the air in the wake, relative to the free-stream air. Take for example, an infinite wing (or a 2D wing). Here, there is no downwash but we still generate lift and have a net downwards motion of the air in the wake. You can see this with online fluid simulators for airfoil sections, many of them are 2D.