I can confirm it is definitely the cable. I also had a cheapo 3-systems-in-1 cable for the Xbox, PS2, and GameCube, which I used with the SNES, and I would get diagonal lines all across the screen, similar to that picture. Then I went ahead and ordered a Monster GameCube S-video cable off Amazon for $5, and the lines went away.
Apparently, it has to do with how they wire the cheap cables. I don't remember the specifics, but it has something to do with the chroma and luma signals crossing over somehow.
So yeah, get a good quality cable, and you won't get this problem.