When dealing with woo, there is no train of logic. What the OP said is correct. Some people believe if you add something to water, then dilute that water to the point where there might be a single part per billion (or even trillion) of that substance in the water, that somehow, magically, the water will "remember" what was put in it and act as a conduit for a "cure" of what ails you.
In fact, when you read homeopathic literature they will tell you the more dilute a substance is, the stronger its potency.
What these scam artists fail to explain is how water can retain this memory of a substance while completely forgetting about all the piss, feces, rotting vegetable matter and dead carcasses that have been run through it over the eons. By their own logic, these substances, by being so dilute, should be exponentially more powerful than whatever they put in the water.