My guess is it just does a simple resample to the smaller sizes (always from the full image capture).
Because Large is 100%, Medium is 75%, and Small is 50%. The 75% would be a sub-sampling problem, and sub-sampling can cause aliasing (moire) and loss of dynamic range. Why not resample?
Either way, smaller is a loss of resolution... but that is speaking of a 100% view. Unless printing murals, we always have to resample (or crop) a 24 megapixel image to use it. Normal monitor screens are at most about 2 megapixels, and an 8x10 print is about 7 megapixels. They cannot show 24 megapixels.
I'd add that Medium size is a choice if you want a smaller file or image, but always leave JPG Quality at Fine. There would seem no point of a lower quality image.
My puzzle is about video format, to 1920x1080. We are led to believe some of the advantage of DSLR video is that it uses the full sensor (allowing Hollywood lower DOF). But Thom Hogan talks like it is a given that the D800 (36 megapixels) subsamples every third line of the Bayer pattern (video). And then resamples that a little smaller. Says the sub-sampling costs two stops of dynamic range for video (ISO 1600 video compares to ISO 6400 still - speaking of D800). Dunno, I've never heard any other mention of that?