Sure, I understand your analogy with Amy and Sandy, but I think it's flawed for the following reason: in a scientific study, the idea is to control the conditions so that you can study one particular variable. So in the case of Amy and Sandy, if you are trying to study which one saves better, you would of course have to control the conditions by saying that Sandy isn't allowed to work, because of course that invalidates the test. But, if you change the terms of the study to be a little broader, and say that you want to study which of them is "better with money," then it would be fine for Sandy to work, since working and earning more money is part of her financial policy, and at the end of the study you would of course find that Sandy (organic farming,) who did something to improve her financial condition, was better off than Amy (conventional farming,) who just lived off what you gave her but didn't do anything to improve her situation.
So maybe you can see that in this case, the validity of the study really depends on accurately stating, and controlling, what it is you are trying to study. In the case of the soil study (to get back on track,) the same holds true: if the study was to determine which method of farming is better for the soil, then adding manure and compost are totally fair since they are an integral part of the method of farming which was being studied. If the study was trying to determine, in isolation, which method of farming is more detrimental to the soil, then you would have to control for that by not allowing additives - but you also would have to not allow the no-till farming to add any fertilizers or any other additives that might bias the results. Which, to me, seems like you wouldn't be getting a very accurate picture since neither approach is representative of the way people really grow crops - at that point you're pretty much just throwing some seeds in the ground and saying "let's see what happens."