I hear a lot of "bro history" facts that may or may not be true. One of them is that a reason the American army was so successful against Germany's is that American units could make decisions for themselves whereas German units had to wait for instructions constantly. Is there any truth to this?
No, in fact, the German army in WW2 was the very opposite of this, Wehrmacht doctrine explicitly called for small unit leader autonomy and the principle of mission based leadership. Which meant that higher level commanders are to simply present to junior leaders an objective and timeframe ( a mission), and the junior officers are to independently decide how to best accomplish it. The doctrine of Auftragstaktik was central to German military theory. The US army in fact sought to emulate this practice from the Germans.
The Soviet army OTOH, at least early in the war, suffered from the problem you are describing however.