"Complementary and integrative medicine" is often presented as an additional option alongside conventional therapy. It was known as "alternative medicine" until recently, with alternative therapy practitioners using "complementary" and "integrative" to make their practice seem more scientific.
Most alternative treatments lack significant evidence of efficacy, with therapies such as homeopathic remedies being little more than water (and perhaps alcohol, depending on the product). Patients may seek alternative treatments because of a perceived gap or failure in their conventional treatment (undesirable side effects, duration of treatment is too long, condition is chronic without a cure).
The renaming of alternative medicine to "complementary and integrative medicine" is a significant shift in that it has been recognized that alternative treatments should be used in addition to conventional treatment options (i.e. the treatments with scientifically-proven efficacy) if they are to be used at all. Practitioners of alternative therapies should not recommend that patients solely rely on the alternative treatment, because the alternative treatment often has no therapeutic benefit to the patient.
The problem arises when the alternative therapy practitioner recommends that the patient solely uses their alternative treatment (i.e. the patient discontinues conventional treatment). In addition to being an additional burden to that patient in terms of time and money, they are no longer receiving a treatment with scientifically-proven efficacy.
There's an article at the Science-Based Medicine blog that looks at "Homeopathic Vaccines," which is a great example of this problem. Link: http://www.sciencebasedmedicine.org/index.php/homeopathic-vaccines-revisited/