N=19 is a very small sample size. I would be careful forming opinions based on this study.
http://www.joponline.org/doi/abs/10.1902/jop.1972.43.3.181?j...
If the data source we tap is valid (i.e.: it does give us the information that we really need) then we need a big sample size to gain precision. If, otoh, the data is not valid in the first place then neither a small nor a big sample size are helpful.
It's a common misconception that the conclusions of a large study always are more trustworthy than from a small study. A larger study will however be able to detect smaller effects and will, as you mention, provide more precision.
What you seem to be referring to is whether or not a sample is representative of a population, which is indeed a critical factor in statistics, but not really related to the issue here.
That depends on quite a few things, and so far none of the psilocybin treatments are controlling for those. It's possible (likely, even) that if psilocybin is approved for treatment and used as often as other meds we'll see effectiveness plummet.