Being a scientist, I would ask for the tests that show GM products to have a low risk of causing harm to the human body.
Could you clarify how these tests would not be a proof of the null hypothesis? How do you define "low"? I share your distrust of corporations, but asking every product to demonstrate that it's never harmful is obviously impossible. "Low risk" is going to be subjective; more helpful would be, say, the number of people in a study, the time followed, a difference in overall mortality and the statistical significance of that difference. I think most people would agree that GM foods are not dramatically harmful (eg drops of life expectancy by decades), so presumably to have the statistical power to detect "low risks" we're talking about a large (100s? 1000s?), long (years? 10s of years?) controlled (don't get to eat what you want) study. People tend not to sign up for those, so if that is your level of comfort you're probably just asking GM products to be shelved. I recognize that is a request/demand for many people.
The same issue can be applied to many other technological concerns; cell phone radiation, high voltage power lines, plasticizers, etc. Some of those have been addressed by epidemiology (eg HV lines / transformers), and some have shown statistical risk in animal models (bisphenol A). You have requested human data, though, and as mentioned above I don't think you can get adequately powered controlled groups of people for food consumption like you can for power lines or transformers, where you can at least segregate groups by proximity to EM fields at the place of residence. If you have a specific substance you suspect of causing harm, you can try to correlate presence of the substance to risk (for example, with, bisphenol A). If you could find a distinct chemical marker related to the GM product (ie a substance that remains in the human long enough to be sampled), then I think you could do a nicely powered study for even reasonably low risk. It's not clear what this correlating substance would be, though; I don't think the transgene, in either DNA, RNA or protein form, would be detectable in a human consuming the food.