Except that the tinnitus loudness is ultimately measured by audiology. So barring any false reports in the minimum masking level assessment, it will not change the outcome of the results.
The placebo effect is not something imaginary. The effect is actually measurable. There have been reports of people recovering from all kinds of ailments when given only placebo, even cancer. And they don't just THINK they get better. They in fact DO get better.
I sugest a google search on placebo, just so that you know what it really is.