There's a difference between median and mean. While both can be called "average", that term almost always means "mean".

If there are 9 employees making $30K/year and the owner makes $270K/year, then the average salary is $54K/year, but 9 of the 10 people are making below average.

Bill Gates made, what, $10 billion last year? Put him in a city with 100,000 people making $100,000/year. His arrival would cause the average salary to double, and all but one would have a less than average income.

If you have 3 people, one makes $97, the other two make $1 each, avg income is $33, and most people make less.

Not saying the parent statement is correct, but definitely not a mathematical impossibility...