Yeah, they should use median instead of average.
Median and mean only diverge when there's a long-tail scalar that skews the mean away from the median. Since rank ordering gives every individual the same weighting with no scalars, "average" is accurate enough, if somewhat colloquial.
I'm not trying to be an ass, I just have always wanted to have a discussion on this. I commonly hear 50% of people are below average intelligence, for instance. But it seems like IQ is a somewhat discrete scale and quite a few people are within the error bars of being exactly average. If you can't tell, I've never taken statistics.
In most cases, with the amount of data you have, the rounding washes out any real impact of the effect, and you often have measurement error far larger than it anyway.
But yeah, if you're ranking 9 people on an easily knowable stat, then technical 4/9 are below median, 4/9 above, and 1 is exactly median.
With the IQ example you gave, it's just that people don't speak with that level of precision about most things--also, that level of precision is very rarely useful.
So, you're not wrong, but kind of sideways to the discussion at hand. It's actually a common problem in business, where really detail-oriented analysts miss the forest for the trees over stuff like this.
Regarding median vs mean vs average (as the 1st reply to your comment mentioned), median and mean are generally equal as long the values being measure are symmetrically dispersed around the "average". If you get a fat tail in one direction or the other, the mean will be skewed in the direction of that tail, and you need to be careful.