Placebos, sure. The thing that bothers me about placebos is the time variable. A course of placebos or drugs is also a course of time. Things heal in time, healing may have happened anyway in that time if nothing was done for those patients. Our immune system is pointed in the healing direction by nature, but significant momentum in that direction is another matter.
My own opinion on mind over body is not one of miraculous healing but of providing good conditions or foundation for healing to happen. I'm not convinced the mind on its own can deal with something like cancer without significant help (proper help, not placebos or psychedelics).