Why does grounding the negative line to the earth eliminate the noise in circuits?
Its not the fact that its the grounding to earth that causes the clean signal... its the fact that your references are now the same.

Voltage is just a reference between two points, what you are experiancing in the first case is called a floating ground.  My connecting the ground of the device you are measuring to the ground of the probe you are in essence telling the two devices (your OSC and the unit your testing) that this is what you define as "0V".