There is a partial truth to the claim, but it is still mostly inflated. Stress is a surprisingly important factor in our body's ability to ward off infections and viruses, but it is most certainly not the sole reason for the outcome. Regarding cancer, the causal link between stress and cancer seems weak, but stress can cause people to engage in activities which increase their cancer risk (smoking, unhealthy eating, etc). If you want to include stress as a "cause" for disease if it contributes to an unhealthy behavior which is directly correlated with a disease (stress => smoking => lung cancer), then the claim is easier to validate.
The association of psychosocial stress and bacterial vaginosis in a longitudinal cohort - "Increased psychosocial stress is associated with greater bacterial vaginosis prevalence and incidence independent of other risk factors."
Can psychological stress cause cancer? - "Evidence from experimental studies does suggest that psychological stress can affect a tumor’s ability to grow and spread. For example, some studies have shown that when mice bearing human tumors were kept confined or isolated from other mice—conditions that increase stress—their tumors were more likely to grow and spread (metastasize). In one set of experiments, tumors transplanted into the mammary fat pads of mice had much higher rates of spread to the lungs and lymph nodes if the mice were chronically stressed than if the mice were not stressed. Studies in mice and in human cancer cells grown in the laboratory have found that the stress hormone norepinephrine, part of the body’s fight-or-flight response system, may promote angiogenesis and metastasis."
Chronic stress results in glucocorticoid receptor resistance (GCR) - "After covarying the control variables, those with recent exposure to a long-term threatening stressful experience demonstrated GCR; and those with GCR were at higher risk of subsequently developing a cold."