Dextromethorphan is definitely not a placebo. Take enough and you'll go to space and meet God. Smaller doses produce euphoria and dissociation, which, even if they don't make the cough go away, makes it easier to tolerate a cold -- same reason antitussives have historically contained alcohol, cannabis extract (which may incidentally work as bronchodilator but was not the reason I imagine it was in antitussives) Funny…
It definitely works for me. It'd be wild if for all 44 years of my life, it's only worked because of the placebo effect.
The article mentions phenylephrine, and that shit definitely doesn't work. Not even a placebo.