This quotation isn't technically true. There are actual costs that do vanish depending on who you contract to. This is completely independent of quality. They are orthogonal.
The sacrifice is characterized as a guaranteed drop in quality if costs are lowered. No. When you sub contract quality is just harder to control. You are rolling the dice. But depending on the sub contractor there can even be an increase in quality along with a cost drop.
For example: iPhones. Subcontracted to china. But pretty high quality. Of course apple had to move over qc to china but there was still overall an up in quality with a cost drop.