The median in a set of values is a useful measure of ‘typical-ness’, and is often seen in news stories involving comparisons of numbers and data
But it is not the same as its cousin the mean, which is what we typically mean (no pun intended) when we say ‘average’  (in a usually- relatively-minor misnomer.)
The median is a MIDDLE VALUE – the place where half the data is above and half below.  That’s its purpose, as a measuring indicator (and is therefore often more useful than ‘average’/mean).  If the data changes, so will the median (and the mean, of course), but the nature of the median is there will ALWAYS be (roughly) 50% of the data below it.  There will always be a median salary, but there will always also be half the population making below that number.  That’s part of the point.
So the candidate’s comment is reminiscent of Garrison Keillor’s quip something to the effect that all of Lake Wobegon’s children were ‘in the upper half’.  🙂 

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Extra, for free:  There is a third often-used measure of ‘typical-ness’.  It is called the mode.  The mode is the value that occurs most often.  (If you want to know, say, the most popular shirt size for men, you certainly don’t care about ‘average’ [mean] or a value in the middle [median] . . . you want the value that occurs most often [mode.] )