Our consumer hotline gets this question periodically. Someone will have come up with a new way of treating some ailment, only to find that insurance companies don't want to cover it.
Insurance companies are far more likely to cover a treatment is it's "evidence-based. Typically, a treatment is deemed evidence-based after extensive clinical trials, for which the inventor (or inventor's company, actually) usually pays. In the scientific community, evidence-based treatments are considered more reliable, and therefor a better value for insurance companies' money -- and more likely to lead to success for the patient.
That said, insurance companies can pay for any treatment, so there's nothing stopping them from covering a treatment that's not evidence-based. However, with many health conditions, there are already numerous treatments available.
If you're a patient, and your insurer is refusing to pay for a particular treatment that you think would be effective, see our "How to appeal a health insurance denial" guide. You can win an appeal, but it takes some work.
Also, here in Washington state, the health plans we regulate -- which are about 37 percent of them -- must, by law, must include access to every type of licensed medical provider. Meaning that if you want to see a naturopathic physician, chiropractor, physician, acupuncturist, etc. for treatment, the choice is yours, so long as the treatment is within the scope of their practice. The law doesn't change what health conditions are covered by your plan, but it gives you more choice in who -- i.e. which kind of provider -- will treat you.