If a gravitational theory derived from a metric has metric induced by a scalar field, it is called Nordstr"om's gravitational theory. Einstein claimed that light does not bend in Nordstr"om's theory. The article shows that light does bend in the scalar gravitational theory if light travels along geodesics of the space-time with a scalarmetric. If the scalar theory is understood as describing a field's geometry, not space-time geometry, then light does not travel along geodesics of the gravitational geometry. Lightdoes bend e.g. when passing close to the Sun, but this is caused by matter in the space around the Sun. The article concludes that there are no good reasons to think that light should travel on geodesics of the gravitational field. The article also refutes the geodesic metric for a small test mass and therefore also Einstein's correction to the precession speed of Mercury's perihelion.