The Unruh effect and a closely related form of PCT-symmetry have been proved in general for finite-component Wightman fields by Bisognano and Wichmann. While this result incorporates most of the fields occurring in four-dimensional high-energy physics, there still are field theories of interest that are not covered (e.g., low-dimensional anyon fields and infinite-component fields). From the spectrum condition, Borchers has derived a couple of commutation relations which 'almost, but only almost' imply the Unruh effect and PCT-symmetry. We show that this result does imply the Unruh effect and PCT-symmetry provided that the operators involved in Borchers' commutation relations act geometrically on a local net of observables.