OG,
Not exactly true - the higher the airspeed the lower the wing AoA and the lower the downwash angle at the tail (which is usually about 40% of the wing AoA)
Plus of course the fact that downwash doesn't change the force on the tail needed to balance the airplane - it just changes the tail/body setting necessary to generate that force.
Pilot's Handbook of Aeronautical Knowledge Chapter 3 - American Flyers
Even though the horizontal stabilizer may be level when the airplane is in level flight, there is a downwash of air from the wings. This downwash strikes the top of the stabilizer and produces a downward pressure, which at a certain speed will be just enough to balance the “lever.” The faster the airplane is flying, the greater this downwash and the greater the downward force on the horizontal stabilizer (except “T” tails). [Figure 3-13] In air-planes with fixed position horizontal stabilizers, the airplane manufacturer sets the stabilizer at an angle that will provide the best stability (or balance) during flight at the design cruising speed and power setting. [Figure 3-14]
If the airplane’s speed decreases, the speed of the air-flow over the wing is decreased. As a result of this decreased flow of air over the wing, the downwash is reduced, causing a lesser downward force on the horizontal stabilizer. In turn, the characteristic nose heaviness is accentuated, causing the airplane’s nose to pitch down more. This places the airplane in a nose-low attitude, lessening the wing’s angle of attack and drag and allowing the airspeed to increase. As the airplane continues in the nose-low attitude and its speed increases, the downward force on the horizontal stabilizer is once again increased.
fig 3.13 and 3.14
http://www.americanflyers.net/aviati..._3-2_img_6.jpg