Millions of people will swear by Robitussin and all the other knock-offs everytime they have a respiratory episode.
I would imagine it doesn't work in some people -- but it works in too many people for it to be dismissed as just a placebo effect. But it pretty much is as innocuous as one can get to the literal placebo tablet. That's why it is an effective expectorant.
The greater implication is that if it works by thinning the mucus in the lungs, it would not just limit its action ONLY to the mucus in the lungs -- but would have that favorable effect on the mucus throughout the body.
Robitussin has dextromethorphan, an isomer of codeine, which is an effective cough suppressant. Thats different than an expectorant. It has been shown effective in randomized-controlled, double blinded studies.
Guaifenesen, on the other hand, has not been shown to be significantly different than placebo in a lot of RCTs so you do have to use your imagination for these things to work.
Have you tried drinking a fresh glass of your own urine by any chance? That'll make you expectorate.