I'm surprised to see your comment down-voted. I think that you precisely summarized the problem. Applying population statistics to individuals is problematic.

However to expand on that I think it is primarily a problem with point statistics. If a Bayesian philosophy was followed, it's about looking at the plausibility of the entire space and realizing an individual can fall anywhere with a non-zero plausibility (or even in some cases an individual can even fall into an area of 0 plausibility given that it is a model and not reality).