I think the reason IAH corrected (or misunderstood) you is because you meant vertical height when reclined, as opposed to height when not reclined ("length").

If the vertical distance from top to bottom of the backrest is 8" when reclined horizontally 8" with a recline angle of 135 degrees...then the height of the backrest itself is 8 * sqrt 2 = 11.3 inches or so.