Earlier quoted context omitted.
Yes. You would have to have a placebo controlled test to confirm placebo vs "just happens to last 8 hours". This is what placebo controls are for.
I generally agree. The secondary (and more interesting) question is whether placebo effect is applicable to infants. Based on the theory of how placebo works, it seems it might not be. It seems there are no studies on that. At least I couldn't find any.
More commonly though, the placebo effect is just natural progression of the disease, errors in data collection (such as patients trying to be helpful and confirming that vague symptoms have somewhat improved), or errors in data analysis (such as lab techs thinking they've seen something in the sample that they expected to see there).
The psychological effects may or may not apply to infants - that's a somewhat separate question. The other effects definitely do - it's perfectly plausible that a lab tech looking for an improvement in an infant's blood sample after treatment "finds" it.