Bear in mind that Ancient and Medieval China are such broad time spans, all manner of Chinese armies have been present. I know most about Early/Ancient China, and can firmly say that this is rather untrue, and that at several long periods of time, there have been willing, trained, and decently armed peasants drafted for service, while at others there have been professional armies.

To begin with, the Western Zhou dynasty was based upon a warrior aristocracy, with the "Great Affairs of State" being war and sacrifice. That famous statement comes from the Zuozhuan, and expresses the sentiment that the aristocracy's purpose was for war, and that war was for their ancestral sacrifices. These were chariot riding armies, with retainers and drafted lower elites/peasantry/slaves sometimes forming their retinues as well, but they were mostly aristocratic.

As we progress to the Warring States period, mass infantry conscriptions becomes commonplace. While early on these armies could be described as "unwilling" and "untrained" (Sunzi's advice to do battle with the army's back against a river stems from the fact that these armies were barely trained and undisciplined at the time), as time progressed methods that we describe as legalist start spreading. These measures introduce things such as mass conscription by corvee, joint punishment in battalions of five, pay dependent on the number of heads/left ears soldiers obtain, land grants, and social rank for military service, it resulted in mass armies made up of peasantry who were certainly willing, trained, and decently armed. And in fact these types of armies helped the state of Qin conquer the other warring states and become an empire. Into the early Han, all the way until Wudi, these types of armies were still the norm, as Han built most of its institutions upon the Qin's. But the emperor Han Wudi changed the nature of the army. Upon successfully conquering the Han Kings, Wudi turned his attention to the steppe. A mass peasant army was no longer needed, and indeed, dangerous internally. So Wudi, wanting to focus on the steppe, chose to absolve the military corvee and change the army over to a professional army, reorganizing the empire's economics in the process. In addition, they paid and hired steppe nomads to augment their army with cavalry and play 'barbarians against barbarians.' This type of army was used during the Han-Xiongnu conflict, which lasted for about 200 years (133 BCE to 89 AD). The Han dynasty, if we include the eastern and western halves, lasted for 400 years, so for half a dynasty's history there was largely a professional army in place.

If we only start counting from when the state of Qin began mobilizing its mass peasant armies with their rehauled incentives system (roundabout 350 BCE) and put the end of professional armies at 90 AD, that's about 440 years of either professional armies or willing/trained peasant armies, which would be longer than the Han dynasty's existence. I dare not speak of Chinese armies in the centuries that followed, but just from an early Chinese standpoint, this perception is largely untrue.

Sources:

Zuozhuan

Sunzi's Art of War

Mark Edward Lewis's State Sanctioned Violence in Early China

Victoria Tin-bor Hui's War and State Formation in Ancient China and Early Modern Europe

Mark Edward Lewis's The Early Chinese Empires: Qin and Han