I actually can see the difference in resolution in the downsampled images.
No you don't. I going to start harping on this kind of statement more and more. What you see mostly is changes in edge acuity.
Well, he could well be. The downsampled 24MP image
should have a flatter spatial frequency response (which might be interpreted as having more resolution - it would make the MTF50 of the combined system occur at a higher frequency). You can see the reason by looking at these graphs (prepared for something completely different, but will illustrate the point here):
The graph shows the lens MTF (the one we're interested here is the f/2 line), the A filter MTF and the combined MTF at a number of different sensor resolutions (actually prepared for an APS-C camera, and the source for the graphs was a bit awry, but the principle holds)
Let's consider as an analogue for 12 and 24MP FF cameras, the 6 and 12MP APS-C cameras. Look at the third graph, the combined response. The 6MP has the minimum of the filter placed at 70 lp/mm. It's MTF50 is about 45 lp/mm. The 12MP camera has its filter minimum at 105 lp/mm, and an MTF50 at about 60 lp/mm. If we downsample the 12MP camera to 6MP with a properly designed digital filter with a sharp cutoff (as opposed to the gradual one of the AA filter) we can achieve an MTF50 much closer to the Nyquist (70 lp/mm) than can be achieved with the 6MP AA filter.
Of course, as you suggest, to do this it is critical to downsample properly, with that sharp filter effect, but it remains true that a 24MP camera can achieve higher resolution at 12MP than a 12MP one can. It is akin to the effect of removing the AA filter, without the aliasing.
