But the ability to efficiently destroy the human body (and protect your own) is intrinsically related to knowledge of how its SUPPOSED to work. It may not have been common for most individuals to necessarily study both directly, but in some instances at least they still draw from the same body of knowledge, and were practiced together at higher levels. The Amatsu Tatara comes to mind, which includes healing skills closely related to its combat techniques. Granted, the Amatsu Tatara covers a lot of stuff, and most examples I can think of are more like battlefield first-aid than full fledged medicine "arts."
Then you are mistaken. Healing and MA were always seen as mutually exclusive. ART as it refers to MARTIAL ARTS simply means SKILL.