We present a method for measuring internal stellar structure based on asteroseismology that we call "inversions for agreement." The method accounts for imprecise estimates of stellar mass and radius as well as the relatively limited oscillation mode sets that are available for distant stars. By construction, the results of the method are independent of stellar models. We apply this method to measure the isothermal sound speeds in the cores of the solar-type stars 16 Cyg A and B using asteroseismic data obtained from Kepler observations. We compare the asteroseismic structure that we deduce against best-fitting evolutionary models and find that the sound speeds in the cores of these stars exceed those of the models.