As both your links clearly state, the possibility of any effect from homeopathic medicines is rejected because of the lack of a mechanism. When comparing water to a homeopathic medicine, the most stringent analysis cannot discern which is which, so of course the human body cannot tell the difference, either.
I think it must remain a mystery why so many people, even very intelligent people who publish in prestigious journals, are vulnerable to quackery.
I think most scientists look at the evidence for things like homeopathy, ESP and UFOs and conclude that scientific experiments will never be sufficiently conclusive to convince true believers, but that the hallmark of a phenomenon that truly doesn't exist is that the evidence never improves over time, and that it never provides any insights that make predictions or that would help identify a mechanism. Predictions are a key part of science, and a missing mechanism is the common element in much quackery.
Another way to look at homeopathy is to think about cause and effect. When you take aspirin, we know it contains compounds that have an effect on the body. Even when we understood aspirin less well (and I believe the mechanisms behind its effects are still not well understood), it is quite obvious that aspirin contains something that can have an effect. There are chemicals in aspirin that can actually do things.
A homeopathic remedy has nothing but water. There's nothing in it that could cause anything to happen. If you drank the homeopathic remedy from a glass, it would contain more soap molecules from the last time you washed the glass then it would of the original substance.
Even the submicroscopic effects of quantum theory are detectable to us. That we can detect nothing that could have an effect in homeopathic medicines should be all you need to know. We do not live in a universe where a substance that isn't present can still have an effect.
Is there any such thing as homeopathic foods? Maybe I should start a company to sell homeopathic liquid sugar. It would be very low calorie. I'll just take a teaspoon of sugar, dilute it 10:1 about 30 times, then bottle it up with a nice label and sell it as homeopathic sugar. All the benefits of sugar with none of the calories or negative health effects!
--Percy