No I think the point that was being made is that the "average person" idea is not that great if you have huge variance. If I have a uniform distribution from 0 to 1, average is '0.5', but its just as likely to get 0. or 1.
My point goes beyond that one: yes, variance is a problem. But _even_ _just_ getting good averages, for all their faults, requires a bigger n than many studies have. Especially observational studies.