Both the article and the interview say that employers "think" that it's cheaper to leave the position unfilled, typically because of lousy cost accounting systems that do not give an accurate picture of the reduced system throughput (and thus the foregone revenue). Most companies optimize locally, which results in de-optimizing the whole system -- a department saves some money by not hiring a new systems administrator until the next fiscal year, and the whole company suffers decreased effectiveness.
Some positions advertised may be, in fact, better eliminated. But that's not the point that the article and interview are making.