This all makes sense. It's a simply matter of bit depth, with 8-bit images there are only so many colors available. If you didn't have noise, you would have gross stair stepping/banding instead which generally looks significantly worse.
The reason you're seeing slight color noise there is that using a bit of color in a dithering algorithm means there are more potential values to use, again this helps avoid banding artifacts. A tiny bit of color noise will generally not be perceptible in most normal cases.
You could try working in 16 bit color instead, that may change how the smudge tool works - just tried that and it looks like color noise isn't used in 16 bit.
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The reason you're seeing slight color noise there is that using a bit of color in a dithering algorithm means there are more potential values to use, again this helps avoid banding artifacts. A tiny bit of color noise will generally not be perceptible in most normal cases.
You could try working in 16 bit color instead, that may change how the smudge tool works - just tried that and it looks like color noise isn't used in 16 bit.