The logical fallacy in that reasoning is the assumption that σ, the surface charge density along the capacitor's plate, is the same in both expressions for the field. That cannot be justified by the fact that the expression given above is "usually stated" that way, since that statement assumes a continuous medium.

In this geometry, it's the field that is constant (homogeneous) throughout, while the charge density is discontinuous at the triple junction. That discontinuity is compensated by the difference in polarization of the two dielectrics.