Probably true. During WWII, there were parts of the German Army that were very mobile. They were the panzer divisions, the motorized infantry, and supporting units altogether organized into a panzer army or a panzer group. They were designed to create or exploit breakthroughs in enemy lines and move rapidly into the enemy's rear while wreaking havoc on their lines of communication before the enemy had an appropriate time to respond. Tanks alone aren't effective unless they have accompanying infantry, artillery, fuel trucks etc right alone them that it was important that the entire formation is capable of moving quickly. It is these rapidly moving units that are typically associated with the word "blitzkrieg".

However only a small portion of the German Army was organized into these panzer armies. The vast majority of the army was the plain old infantry marching on foot. German industry was not capable of providing them with the kind of transport capabilities that the panzers enjoyed. In fact, the German Army relied on nearly a million horses for their logistics.

Thus theyt had a 2 tiered system - the hyper-mobile panzer formations and the slow-moving old-school infantry marching on their feet (sometimes train). This sometimes created problems in that the panzers got too far ahead, creating dangerous gaps in the front line.