How would you do a trial for that? Placebo placebo?
For example, here you have your basic generic white placebo which costs $5 a pill, which we all know is totally worthless because it is made out of sugar. Now, you sir are insured, so if you want you can have this cutting edge blue PlaCeBo (TM) -- just between you and me, it costs like $80 a pill and has nothing in it but sugar but who cares, insurance covers it. Alternatively we have the PlaSeBo which is the cheap Chinese knockoff and hasn't killed anybody this week that we know of, not that that is too surprising, because it is made out of sugar.
'Non-blind' means that patients were informed that the pills they were issued were totally inert, that they were placebos, and in this case they were also assured that despite this the pills would be of benefit to them. The study concluded: 'The primary finding is that patients can be willing to take placebo and can improve despite disclosure of the inert content of the pills; belief in pill as drug was not a requirement for improvement.'
They tell the subjects something that's bound to be confusing to most people. I don't know that there wasn't "belief in the pill as a drug". If the test were done only with subjects with a scientific background, or if they omitted the assertion about the benefit, it would be more convincing.