The way I read it, it has to do with whether you allow a demonstrated flaw in reasoning in one's area of expertise compromise your respect for that expert. A very interesting topic, to me at least.
A lot of knowledgeable people (including doctors who very well know it's inert) use homeopathic treatments instead of placebos. Why? In some states in the US, placebo treatments cannot be purchased without a prescription. Homeopathic treatments are almost always available for a simple purchase.
Wouldn't such a move require informing the parent? Besides, the article describes how the doctor went out of their way to praise the virtues of the medicine provided. If helping with a condition has the side-effect of spreading dangerous memes (yes, homeopathy can be dangerous if appropriate treatment is foregone in its favour) from the mouth of a respected expert, then that is one hell of a side-effect that the parent should be at least made aware of.
True, but the confidence of the patient is instrumental in placebo effectiveness. If the doctor has a long-term relationship with the patient, then they can have it both ways. They can play up the efficacy of the "medicine" then educate the patient on subsequent visits.
As a placebo it makes sense, but my GF once went to a doctor whose office looked like the homeopathic section of a health foods store. There are quite a few doctors pushing this stuff out of ignorance or purely for financial gain. In the case of the doctor I mentioned, I think it was (willful?) ignorance.