I'm not sure where the idea of "self-taught" skills originated. I'm sure it's something that's rooted deep in history and it would be a mistake to assume the origins of the concept started in modern times. In art history there are examples of naieve painters, ones with no formal training, who became recognized for their contributions to art; some that come to mind are Grandma Moses and Edward Hicks.
In the Martial Arts if one pursues a self-taught program of training and then tries to apply their skills in a "real world" arena the consequences are immediate and physical. The consequence of failure in the applications of martial arts skill includes serious injury and/or death.
Unlike other fields of study in the humanities there are no prime examples of self-taught martial artists that are recognized for their contributions to the field. Many people will mistakenly point to Bruce Lee as an example of a self-taught martial artist. That would be a mistake since Bruce Lee was classically trained in Wing Chun kung fu during his early years in Hong Kong. Even when he studied in the United States he sought skilled martial artists to train with and develop his skill sets that later were labeled as Jun Fan Jeet Kune Do. Just because Bruce Lee dictated the direction of his own training and study, that does not mean he was self-taught. He learned from other martial artists, such as Ed Parker and Gene LeBell.
Bruce Lee's philosophy "style of no style" has been hijacked and misrepresented to justify the reasoning behind self-teaching modes in the martial arts. One need only truly examine the life and work of Bruce Lee to understand nothing about the man advocates for self-taught training programs.
If one truly is motivated to learn a Martial Art and has invested a lot of time into teaching themselves then I encourage them to seek out a relationship with a senior or master level martial artist. Once you establish a good working relationship ask them if you can test out your self-taught skills under a controlled enviornment. I am positive you will find self-taught skills insufficient to be competetive or reliable in application. A refusal or fear of testing ones own skills against others is a definite sign one understands deep down they aren't up to the task.
I stand by the position that one cannot learn a martial art without the physical presence and guidance of a teacher; videos and books do not count as "a teacher".