Schizophrenia seems like a unique case, doesn't it? This label seems to have a strong genetic component and also to have some association with the use of drugs (namely hallucinogenics). Also, the symptoms can be more intense, bizarre, and severe in schizophrenia than in, say, the so-called personality disorders. That, it would, seem, is why many "schizophrenic" people chose some form of medication. However, I strongly believe it is possible, with a good, clear and strong therapist, to treat schizophrenia naturally or with alternative therapies. I agree with the point Reality Therapy makes for not diagnosing clients. I have also encountered some very able therapists that could direct someone with schizophrenia by deeper therapeutic work (I am not talking about simple person-centered attentive listening) to a state of psychological health. 

There was a spiritual teacher some years ago in India who would go to mental institutions and pick out patients, and connect them with the truth, with presence, or "reality", and they were, as a result, cured of their supposed insanity. I believe this spiritual teacher's name was Meher baba if you want to look him up.

My feeling is that it takes the right technique and a very advanced therapist to direct the therapy sessions in order to "cure" someone with schizophrenia. I imagine that a technique like kinesiology which incorperates physiology and psychology to release blocks in the body's systems and energy meridiens might be useful. One highly available form of kinesiology therapy is called EFT or Emotional Freedom Technique and can be learned relatively easily to release phobias, traumas, depression, etc. It's a really fun technique for self-treatment of physical, psychological, or emotional problems. Here is link if you want to find out more about this approach:

http://www.thetappingsolution.com/

All the best in your exploration.