On the droid numbers, I will point out that at some point the average person loses the ability to comprehend huge numbers and probably cant tell the difference between say quadrillions and trillions. Therefore it is possible that the strategists behind the war knew that the droid army was smaller, while the general public believed in a propaganda rumor, because they cant really comprehend the numbers anyway.
Aside from that the clone army even at its absolutely smallest estimate was stated as 3 million in Republic Commando and some other sources and has been highly contested ever since.
Also werent the "1 million units" that were ready in AotC later retconed to be battalions of around 100 men rather than individual soldiers?