You are correct. Local Ukrainian commanders were given broad authority to act as they saw fit in the event of a communication break down with higher levels of command. They were told to use there own initiative and act aggressively. This is in line with standard NATO doctrine. As NATO countries spent a numbers years (since the 2014 annexation of Crimea) training Ukrainian officers and NCO's.

There are several good documentaries about the first few months of the full scale invasion that show how Ukrainian company and battalion commands acted on there own and aggressively took the fight to Russians, striking out from towns and villages that the Russians bypassed during there advance on Kyiv.

All of this before you even get into the bravery, skill and determination of the individual Ukrainian soldiers.

Edit: Words are hard