My thoughts exactly. If the same diet is fed to control and test subjects, maybe they both react strangely, but there shouldn't be any measurable difference. Isn't that part of why the results are given as +- .01% (or whatever number they give)?
Margins of error are not based upon stray factors that may affect results, but are rather designed to take into account sampling variation.
Suppose you have a large tank which is filled with black and white beads and you want to determine what percentage of the beads in the tank are white. Both types of beads have similar physical characteristics, and the contents of the tank are well mixed.
Suppose you take out ten beads. Three are white and seven are black. What can you say about the concentration of white beads in the pool? It seems likely to be about 30%, but it would hardly be surprising if it were 22% or 38%. Indeed, it shouldn't really be surprising to find it was really 15% or 45%. It probably isn't below 10%, and probably isn't above 50%, but drawing only ten beads can't really tell you much with certainty. Even if 90% of the beads were black, drawing ten beads at random would yield three white ones about 5% of the time.
Now suppose that instead of taking out ten beads, you take out twenty and find six of them white. It becomes possible to refine ones estimates much more. If I did the math right, slightly less than 1% of twenty-bead draws from a 90%-black pool would yield exactly six white ones. Thus, one can pretty well say the pool isn't 90% black, but one still can't nail down the concentration precisely.
If one takes out a hundred beads instead of twenty, the likelihood that the draw is a major statistical anomoly will go down. And if one takes out a thousand beads, it will go down even further. Note, btw, that it doesn't matter at all how many beads there are in the pool. A thousand-bead sample will be just as good for estimating the concentration in a pool holding a million beads as for one holding a billion, if the beads in the pool are well and uniformly mixed.
If the beads in the pool are not well-mixed, there may be a sampling bias which cannot be eliminated by an increased sample size. Stated error margins are meaningless when sampling bias exists. Indeed, the presence of sampling bias often makes it difficult or impossible to obtain really meaningful results, though it doesn't stop people from putting forth their results whether meaningful or not.