Incorrect to a degree. Knights were nobles, and fought, through a very complicated system called feudalism, for their liege lords. In turn they got property, title, and other benefits. And it was complicated. A knight could pledge to a lord, and to the lord's bitterest enemy. Then when there was a battle, the knight could refuse to fight for either, or fight for one or the other, and they did. Often. Kings had very limited control of knights and they were not instruments of war as much as hired guns. Who quit or changed sides quite often. There were many battles where a lord would wait until he saw which way the battle was going before he went to the defense of a liege lord. They also could afford the latest in war high tech, armor, training, proper helms, excellent swords, and horses. Which gave them the ability to kill large numbers of peasants with no armor and a sickle. The advent of the English longbow changed the face of war. A 175 pound bow could penetrate armor easily with a bodkin.
Chivalry as a Platonic ideal is one thing. It never existed. Chivalry in the early middle ages was neither chivalrous, nor often seen. For the most part, it was propaganda.
It also was, very much, a convenient means of keeping women in their place, in the castle, hearth, and home, casting them as weak, subservient and in need of rescue. They were the victims as much as the beneficiaries. The early middle ages were unbelievably atrocious when it came to human behavior.