Good question, I don't know anything about how MMD works, but my guess is that it has something to do with the rendering process. Someone else who knows more can go into more detail.
They may also be doing some kind of post processing after they've uploaded their videos to clean it up, a bit like what's done with some fansubs to remove visual artifacts etc.
Also probably has a lot to do with the quality of your models. The base models that come out with MMD aren't great compared to the user created stuff,
like this one.