The conclusion by Thiel was not that Clark Zappers kill pathogens but that either the electrical stimulation improves immune responses or aids absorption of the anti microbe supplements the patients were taking.

quotes from the study by Robert Thiel:

The purpose of this pilot trial was to determine whether there may be any efficacy to combining the use of bioelectrical stimulating units with nutritional interventions [vitamin, herbal, and glandular combinations] for people with patterns consistent with chronic fungal, bacterial, viral, or parasitic infections.
My previous research has clearly shown that nutritional interventions can, on their own, result in symptomatic improvement when chronic infections are present [14,15]. This trial attempted to see if adding the intervention of bioelectrical stimulation could result in symptomatic improvement to greater degrees for people with chronic infections. Many of the participants were greatly impressed by the effectiveness of the zapper; some who improved, however, felt the zapper had no effect and improvement was entirely due to the continued use of supplementation.
The results of this study suggest that zapping combined with nutritional interventions may have helped most of the participants improve. Nutritional interventions give the body substances which it can use to improve immune responses [18]. Although this is not certain, it appears that either nutrient absorption is somehow improved [28,29] or IgG (immunoglobin G) [1,19], some T cell (T-lymphocyte), biochemical acid, or some other defense mechanism is somehow stimulated through zapping and thus some segment of the immune system, but not the zapper, destroys the invader.

[14] Thiel RJ. Nutrition to improve the CD4 count of persons with AIDS. National Institutes of Health, Bethesda. April 1997: Submittal NTN B1.
[15] Thiel RJ. Chronic fatigue assessment and intervention. ANMA & AANC J 1996: 1 (3): 17-19.