If this is true, explain to me why all states have come to recognize chiropractic by licensing it and regulating it with laws. The law has nothing to do with science. If enough people are interested in getting a law passed, and do it cleverly, they can get a lot accomplished. Other forms of health quackery have been legalized in a number of states. The state legislatures simply say if you can make it and sell it in the state, then it's legal.
Accreditation has nothing to do with what's taught.
You can get accreditation if you develop the correct form and structure in your school. And that has nothing to do with what you teach. Actually, chiropractic is proof that the accreditation system has a hole in it. The accreditation system worked until chiropractic got accredited. Eventually, the mixers got powerful enough that the educational offices decided they represented chiropractic, and, as a result, one of the principal objections was overcome.