I agree. Similarly relativism can evaporate some pain. You can feel pretty bad if you think you're alone in a situation. Just knowing someone went through the same issue relieves part of the pain, even though nothing changed in your life.

Which begs the question: If placebos (sometimes) work, (particularly when administered in hospital settings and when expensive, at least in the eyes/brain of the patient) is it unethical to administer/provide them?

Placebos work even when people know it's a placebo. We might want to establish a baseline, like the pretender has to remind the patient he's just a pretender once a year. But if a pretend doctor can help, then go for it.

It is unethical to say that you are administering a medicine when you are not doing it, except in trials to which the subject has agreed.

I 100% agree, but that doesn't mean we can't still administer placebos:

I've read elsewhere that you don't have to lie to the person to still have a successful placebo effect- they can still receive a benefit even knowing it's not a real drug.