This has nothing directly to do with sample size.
First, that's obviously not a rephrasing of what they said. They, very clearly, illustrated a valid case for a well-powered, low sample size study. They presuppose a case where 31 virtually identically-haired white men undergo a treatment and, voila, it works decidedly well.
Second, you're begging the question. You state that the drug doesn't work, yet have concocted a scenario in which it clearly and explicitly works. Even in your "cheatsy" example, 15 of the 16 people go from "bald" to "full head of hair." If the "full head of hair" metric is wrong it has nothing to do with the sample size, rather, we'll find this by examining how the study partitioned groups, pre-trial measurements and its claims to have calculated effectiveness over placebo (ie: actually reading the study).
Third, you've neglected statistical power (which is actually your argument here) for an incorrect statement about low-sample size bias. You state that the mechanism of action for this bias is a pre-partition between [truly bald, nearly haired] and then, given maybe a bit of luck, let good ol' father time take over and show, wow, the (useless) drug works! Maybe everyone experienced a 1.5x follicular density growth, but only because you've been able to presort the group do we see the non-placebo benefit more than the other... except this has nothing whatsoever to do specifically with sample size! If you can sort a trial with 31 people into 15 "truly bald" and 16 "near-haired" you bet you can sort a trial of 200 participants into 96 "truly balled" and 104 "nearly haired" or, heck, just don't even randomize your group selection at all! Or run the study 20 times and pick the successful one! Or any number of other tricks, which are real and meaningful and require someone to actually read the study to uncover instead of just looking at a clearly, very misunderstood, number.