Yes, looks like that light transport limitation regarding lights in glossy reflections. You could try enable visible in reflections for the light sources, that removes the "shadows" from them. In this test scene at least, you could also change the cylinder that is the light fixture, by using a RaySwitch with nothing in the Reflection Override, too, as it's the combination of the light, the object behind it that it is occluding, and the glossy reflection that causes the issue (if you hide the cylinders, the "shadows" - which are reflections actually, if they watch how they move when the camera moves - disappear).