My approach is don't argue directly against personal anecdotes. Inevitably, this puts you in the position of making claims that you can't easily justify. In fact, it's probably a good idea to explicitly acknowledge that you can't explain what happened, because you don't have the necessary information.

After that, here's a suggestion: Instead of falling back on phrases like "placebo effect" or "scientific consensus" or "laws of physics" - these just aren't convincing to people who aren't already on the skeptical team - meet a story with a story.

"Some scientists in Japan once did an experiment on kids who were allergic to a plant called a lacquer tree. They blindfolded their subjects, then rubbed one arm with lacquer tree leaves, and the other arm with harmless chestnut tree leaves. Of course, the kids developed a rash on one arm and no rash on the other.

"But here's the thing: The researchers lied about which leaf was which. And the rashes showed up - real rashes, red and bumpy - on the arm that got the harmless leaf, not the arm that got the poison leaf.¹

"So maybe what cleared up your son's rash wasn't the medicine he was given, maybe it was the story he was told. Maybe it would have worked just as well no matter what the medicine was."

And that brings you right back around to talking about placebo-controlled trials, which is where you wanted to be in the first place.