This may be possible in some medical fields (I doubt it), but not radiology. There is simply too much to learn. I completed 4 years of medical school followed by a 5 year residency. Some radiologists go through additional sub-specialty training. I've been practicing for 5+ years, and I'm still learning everyday.
I am a doctor's doctor, meaning my customers are doctors from every specialty, who order studies and read my reports looking for answers they can't answer clinically. I can talk to Orthopedic surgeons in their language, Neurologists in theirs, and Gastroenterologists in theirs. I'm familiar with the radiological manifestation of most pathological processes a human can experience.
The notion that someone could self-teach what I know seems impossible.
There are licensing and board requirements, but conspiracy theories aside they are not designed to create artificial scarcity, they're supposed to keep dangerously ignorant doctors from practicing.