Lake Woebegon effect is such a terrible name. It is very easily possible that every student in a small town is above average compared to e.g. the national average.
Did you spot one here?
> I have a basic understanding of statistics
Perhaps an intermediate understanding would help. Entire schools tend to score higher or lower together, also wealth correlates to IQ and scholastic success and zip code. There are also other reasons an entire group would be biased higher or lower.
> I deal with this kind of sounds-good-if-you-don't-think-too-hard "insights" all the time
Uh-huh.
I disagree with this argument, but that's the basis of it.
Just my crazy version of what "easy" could entail.
Firstly, you're assuming independent probabilities between the students.
If it's a single class of 30, for certain skills it might be much more likely than pow(0.5, 30) if they were all specifically coached on that particular skill, or if there are selection effects impacting what type of person ends up in that group of 30.
Secondly, even if we grant the assumption of independence, the claim doesn't rely on "unlikely values for ... small". There's many small towns with a student body of only 5 or less people, and pow(0.5, 5) isn't that unlikely.