Kyoukaku 侠客 were a real thing, though somewhat clouded in fiction as the concept took on a metaphorical vibe. For example, the yazuka organization Kokusuikai 國粹会 extolled the ideas of chivalry and using bushido to combat "the corruption of national morals and beautiful customs" while promoting "harmony between labor and capital." That was the early-mid 1900's, but the idea goes much further back.
At the turn of the 17th century, Tokugawa Ieyasu came to power and the "age of the samurai" began to close. In some ways it was thought that the samurai's ability to use force to solve problems symbolized their sovereign autonomy. Tokugawa's government intervention to restrict such outbreaks of personal honor violence generated a cultural shift. These acts, often called kenka 喧嘩, could be categorized as the stereotypical battle for honor: based on an anger that was a deep, heartfelt emotional response... whether justified or not. Hypersensitivity to "insults" is a much larger discussion! What's important to understand is that this was a deeply cultural idea, and the government's clamping down on kenka and other quarrels acted as a culture shock in my opinion.
From the late Kamakura to early Muromachi, the concept of jiriki kyuusai 自力救済 existed. It was a legal allowance for recovering one's honor or goods without recourse to public law (lit, "self preservation"). While not necessarily looked upon favorably by society, it did exist as a way to take the law into one's own hands- helpful if the offended party could not rely on public law. Later on, this legal notion changed to kenka ryouseibai 喧嘩両成敗, or equally severe punishment for all parties to a quarrel regardless of the reason behind the conflict. This legal world manifested in the late Muromachi and Sengoku Jidai. Tokugawa's pacification complicated things entirely and was meant to keep two social organizations from escalating conflict due to honor-bound reasons. This coupled with the demilitarization of the samurai, destruction of the feudal structure (daimyo vs central government, separating samurai from land ownership, etc) threw people for a loop.
Different groups of people felt the need to rebel. For example, kabuki mono 傾奇者, literally "strange/crazy people/things," appear in the early 1600's. They were known for aggressive, violent, and unruly behavior. They were the unruly rock and roll in a time of classics... and often not the nicest of people. This contrasted with the idea that emerged of kyoukaku; whereas kabuki mono were rough and not well liked, the concept of kyoukaku took the rebel idea and added a more "positive" spin. They would still use violence, but the idea was the violence had a morally superior purpose. Whether this was the truth or not often varied, and places of employment for such individuals (gambling parlors, brothels, etc) didn't help with government favor. It definitely wasn't as nuanced as what one might find in classical martial arts where ideas like katsujinken 活人剣 and setsuninto 殺人刀 (the sword that gives life, the sword that deals death) can be found. Still, the concept of a "rebel with a cause" has always been an attractive one and its birth as a result of the Tokugawa's pacification "culture shock" shouldn't be too surprising.
I'm not sure if there is a clear kyoukaku "Robin Hood" individual in Japanese history. Often times Ishikawa Goemon is considered a Robin Hood equivalent, but he was a ninja and not a kyoukaku.
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