You’d think that, but there have been studies where the subjects have been explicitly told they were receiving placebos, and still had positive effects.
In fact, there is a woman who was told essentially “this is a study to see if placebos can help with IBS, here is your placebo, it should do nothing.” And they helped her to the point that she begged to continue receiving the placebo pills because they helped her.
So it’s not just a feeling, or a mindset. There’s something to placebo we still don’t understand.