From a reader (and Poli Sci Prof):

I know you don’t actually care, but you were almost certainly
right the first time.
If half the population has a below-median intelligence (true
by definition);
If intelligence has a lower bound (0 IQ/ brain death/ etc) but
no necessary upper bound, or even just an upper bound that is
further above the median than 0 is below it and that trails
off gradually (i.e. there are geniuses and a few super-geniuses);
and if intelligence has an otherwise roughly-normal
distribution (a bell curve, which is a perfectly ordinary
fact of probability and carries none of the baggage of The
Bell Curve);
In short, if the distribution of intelligence is a
left-censored bell curve (a bell curve truncated at 0 on one
side but exhibiting normal trailing-off properties on the other);
then mean intelligence is higher than median intelligence.
From this it follows that *more* than half the population has
below-average (meaning, as your correspondent insists,
below-mean) intelligence.
Really.