There are many influences on the human body, and the mind certainly place a major role. I have written major sections in three books of mine to this matter. The conscious mind does influence the body through the well documented mind/body responses. Even more influential is the subconscious mind which translates its many memories into constant bio-chemical changes in the body. Nearly 200 studies have documented that the body responds to emotions in an instant. For example, the DNA of medical students who are sitting for an exame have a much lower interleukin and interferon secretions (anti cancer and antoi viral drugs) than when not tested. The levels remain low for a while when the students know they have failed the test. THose who know they have passed the test, even have a higher output of these drugs to compensate the previous low secretions.
In other research, the double strands of DNA molecules tighten and their codons reduce protein-production when they are exposed to angry or fearful emotions. They relax and elongate, while their codons return to normal activity, when the researchers produce or experience emotions of love and joy. The effects are immediate. The more permanent genetic alterations occur due to constant exposure of the body to negative thoughts, feelings and emotions. Genes don't change or mutate by mistake. They only change when the environment changes, such a presence of medical drugs, alcohol, chemicals, food additives, toxins, and the biochemicals produced in response to fear, anger, jealously, etc.
The most obvious mind-over-matter scenario occurs during the fight or flight response. The released adrenalin tightens and squeezes those blood vessels that supply all the internal organs and dilates those that supply the muscles and bones, which is necessary so that you can fight or run away. People who are exposed to constant threats, inner or outer, are under the influence of these stress hormones nearly all the time. This undermines the most basic functions in the body, from blood circulation, digestion, breathing, matabolism, to waste removal.
To answer your question, a person who eats unhealthy foods, but is of a happy disposition, can even turn poison into nectar, whereas an unhappy person who eats the most wholesome foods turns nectar into poison. I have met people in my life with extemely healthy constitutions, who ruined their body's by not loving what they were doing, and become very ill. On the other hand, I have met very sicl people, who began loving their life again, and became extraordinarily healthy. It all comes down to the personality and mindset of the person. In Timeless Secrets of Health & Rejuvenation I describe the personality and emotional states of people who develop cancer. The question to ask is not, "what is cancer," but "who makes it." This applies to almost all other diseases as well.