If, by "modern healing practices" you are actually referring to alternative medicine (in the form of Naturopathy, et al.) then the reason why some people and medical agencies have a hard time accepting it as a good practice is because alternative medicine scarcely has enough scientific foundations upon which it can build a good and steady reputation for being effective, or safe. As a result, medical insurance plans (and now the government-based medical assistance program) just cannot gamble or take the risk to cover treatments done with methods that cannot be correlated to actual scientific results; especially when millions of Americans will be in need of some form of medical coverage in these very unhealthy times.
This does not mean that "official" modern medicine is the best that there is, either. The medical community has spent billions of dollars in potential cures and treatments for cancer, AIDS, and even the common flu without any kind of success, nor with any hope in the horizon. Moreover, as new diseases and allergies keep flaring up, it seems as if the currently accepted methods "de rigour" are a mere repetition of practices that are leading us nowhere.
However, alternative medicine does not always prove to be the best alternative to current accepted methods, either. This is because, regardless of its claims of success, it still lacks the validity and experimental research that exists in the true scientific community. Without enough experimentation it is impossible to determine the effectiveness of a treatment. What is most important, alternative medicine does not always concede information about actual findings of how they can kill you if a patient mixes alternative medicines with prescription drugs. That is only one of the many things that may make alternative medicine dangerous: people who practice it may not know as much about its effects as they think that they do.
But THIS is what settles the deal: The Food and Drug Administration does NOT have to hold alternative medicine accountable for what it does to the public because Alternative Medicine is NOT a practice that is regulated. Anybody can come up with a cup of dust and claim that it is magical and that it can cure diseases. Bottle it up, sell millions, and then disappear. No questions asked.
Conversely, every single "discovery" that comes from the medical field is regulated, analyzed, tested, and peer-reviewed for validation. Experiments are conducted over and over to ensure some form of success. After all, an alternative "medicine" doctor is not ensured for malpractice- but regular medical doctors are! In fact, physicians often spend more efforts ensuring that their treatments ARE effective precisely to avoid being held accountable of malpractice and losing a license as a result!
Hence, the lack of validity in terms of testing and experimentation, plus the lack of regulation that alternative methods suffer are the main reasons that render them less believable (and perhaps even less reliable) than traditional healing methods that are scientifically-tested by a community of professionals. At least, that is as much as we can claim!
Therefore, there is little that care providers can do to help people accept alternative medicine. The only way to be able to buy people into it is by showing, with proof, that it is in fact a safe and alternative method to current medical practices.