Why is it easier to inverse transform every object in a scene than to transform a camera? My lecturer for a computer graphics (raytracing) paper has stated that 'It is easier to apply the inverse transform to the world than it is to apply the transform to the camera.' The example given was that is it easier to shift all objects in a scene 5 units to the left than it is to shift the camera 5 units to the right.

This seems to imply that it's easier to iterate through and transform multiple objects in a scene than it is to apply a single transformation to the camera. 

Is this correct, and if so, why is this the case?
That's actually incorrect. You can transform every ray of your camera if you wish (and numerous implementations do so). There are some advantages and disadvantages to each method (e.g. if your rays are more than your vertices you end up doing more transformations, however you don't incur cache misses by running over all vertices).