From a physical standpoint, it makes no sense to add two RGB colors.
It makes sense to add two lengths. (1 inch) + (1 inch) = (2 inches).
It does not make sense to add two RGB colors. The result is not a meaningful physical quantity. In the same spirit, (7.8 earthquake) + (8.3 earthquake) != (16.1 earthequake).
This is a big problem for those of us who are trying to reproduce how nature looks on the screen of a computer. (In my case, realtime graphics.)
For the case of the combining beams of light, the only time that the hue wouldn't change is if you have two lightbulbs that emit precisely the same EM waves --- the same frequencies and the same intensities for all emitted waves. This is practically impossible. Therefore, the hue of the combination is never exactly the same. Just because you can't perceive the difference, doesn't mean there isn't a difference.