Business isn’t a monolith and the cost of dealing with new and changing government regulations tends to hit small businesses hardest. To whatever slight extent the overtime pay rules have any bite, they will probably do so at small firms struggling to stay afloat.
Do you see the presumption here? It is that the Department of Labor—not a profit-making firm but one run by people whose wages and salaries are dictated by law rather than markets—is in a better position than the private sector to know what the market demands. That’s implausible on the face of it, unless you fundamentally believe that markets are dumber than governments and that the price system is nonfunctioning.