On another note, I found that old video from GameTrailers from 2008 that had the Forest Mushroom music from Japanese Brawl. The one I said before sounded like it was a Mario Paint remix used on a Custom Stage designed like a Mario Paint face with Mario and Yoshi fighting.
It was reuploaded in 2011.
http://www.gametrailers.com/videos/5yl1le/super-smash-bros--brawl-ssbb-mario-vs-yoshi
However, something I learned about it:
It turns out, it's
fake.
The music was edited in the video (this was before even music hacks were possible), as the song used on the stage itself is the "Opening/Ending (Super Mario World)" song when you look at the song name at the stage intro (in Japanese, of course).
Apparently, the music and face together was an odd Japanese meme, and someone in Japan decided it would be funny to make a video about it in Brawl.
So all these years, I thought I was crazy that I was somehow the only one here that knew what the scrapped Mario song sounded like, just to find out it was all a joke. -_-