It's interesting you mentioned that because I was coming up with the same conclusion (about aliasing). I found this while looking up the various different dithering mods used when downsampling and it turns out that the noise when opting not to use any dithering options is similar to the results I was getting from the DMG.
I'm not sure why though - there wouldn't be any reason for the DMG to increase the bit-depth of the original source but I do find it a bit suspicious. I assume the CPU itself is generating the tones and, if so, I don't think it can be easily avoided without using a lowpass filter (and thus reducing some of the highs you do want). If the DMG uses some sort of DAC though maybe there's a chance
I don't know enough about the DMG's audio pipeline to really say, though the down-sampling just wouldn't make any sense to me and is not something I noticed on the NES so *shrug*
Maybe it is just an interesting coincidence
EDIT: Actually in thinking about this more, vgx already mentioned the GB has some aliasing so that's probably what I am hearing. I'm not sure what causes that with the GB internally yet but that seems to be the likely candidate.