As hard as it is to prove a negative, many times that is exactly the task. For something such as Zapper testing, a huge problem is ruling out all of the other things which might have contributed to, or outright caused, a positive result. If you take 100,000 cancer patients and put them on a rigid diet of 10 bananas a day, some of them will go into remission. Did bananas "cure" them; probably not, but maybe some of them responded particularly well to bananas. Different group of 100,000 patients, this time with zappers. Some go into remission. Was it the zappers, or did some start eating bananas at about the same time? How do you prove that it was *not* a subtle change in diet, in the city's water supply, in their own immune system? And how do prove the positive (zappers) without first proving it was not those negatives?
The answer lies in layers and layers of studies, some very long term, parsing apart the gazillion variables and the gazillion raised to the holy crap power number of combinations. The nice thing about the "medical establishment" is that they have all of those refereed journals with a gazillion studies, many of which reduce some of the variables on the way to whatever they were chasing. As I said in a round about way in the first response, negative hypotheses can be proven, but it takes an enormous amount of work and attention to detail. It takes discipline.