To play devil's advocate for a moment, that really depends on the business' structure. Some businesses are heavy on labor costs. But in general, yes, payroll is typically not a huge proportion of a company's total budget.
But yes; it's silly to argue that a $15/hour min wage will make everything cost twice as much when you've got places that already have significantly higher minimum wages and don't see that big a price increase. We don't even have to rely on theory; we have actual real-world examples that it's a baseless claim.