Don't have a huge ammount of time, so a few points:
1. Thread is shooting off on tangents. Yes, if you change the speed you change the descent rate, e.g if you choose to fly at Vmp in both (heavy and light) cases then you are choosing to introduce an additional variable.
2. The question does not state "at a fixed speed", but then again it doesn't have to. Check the preamble of the LOs, it specifically states:
Normally it should be assumed that the effect of a variable under review is the only variation that needs to be addressed, unless specifically stated otherwise.
As such, the question is asking about varying weight and we can take it as read that the speed is not a variable. If you choose to frame an arguement around varying the speed you just are not ATQing.
3. I accept, that as Dick says, the high speed descent is a 'special' case in that it is not a 'general' solution, however it is the majority case in civil air transport operation. Since alpha is low, lift dependant drag is relatively unimportant and therefore the effect of changing weight on total drag is minimal. This is the case that the question refers to, and also the case that confuses student pilots. My point was that it LOOKs counter intuitive at first glance, but if the student 'gets' ROC = specific excess power (which IS intuitive) then you have a great way of breaking down the counterintuitive barrier.
edit: Looking back, see ther is no 'question' as such, I am referring to the way such things are usually phrased to provide a brain teaser!