There's some evidence this is false. Now, when I tried to google it, this is the only study I found (or at least the only one I could read for free), and I don't trust it all that much. But it is not immediately crazy to think that employers can get more effort out of employees at the lower-paid end by paying them less, eg due to loss aversion.

We have yet to establish that minimum-wage labor meets my intuitive definition of a market, where people can freely make or refuse trades and you get more by paying more.