The median is an average

So is the arithmetic mean

So is the geometric mean

Referring to the median as “the average” is completely appropriate, especially as it pertains to IQ and other things reckoned in terms of estimates of population-level statistics.

I can’t say categorically that the distribution of intelligence is symmetric, but there isn’t a very strong reason to assume it’s especially skewed like there is with—say—individual income, where there’s no hard limit to how above-average you can be, but there is a clear barrier to how below-average you can be (zero income). This is why “median” incomes are specifically identified as such… it matters in that context, but in many other contexts it simply doesn’t matter whether you are referring to the median or the arithmetic mean when you say “average.”