I use organic in this sense to mean evolved from other words which are commonly used together, such as “alone”, which was originally a contraction of “all one”, or adopted from other languages, for example.
For example, orthopaedics comes from the French coinage orthopedique, which was coined in much the same way as chiropractic. However, because it was adopted from another language, there was an existing “declension” to fit it into (insofar as English can be said to have declensions).
If the estimable Doctor (I use the term loosely) Palmer had chosen to, he could simply have used “chiropractic” as an adjective only, and “chiropractics” or “chiropractic medicine” or “chiropractition” or whatever as the noun, but he didn’t.
In a couple of hundred years people will probably have started to do so, assuming their lawyers are still sending them to see quacks.