In a Delta-Sigma ADC, does noise shaping bring the noise to the signal's frequency?
The mistake you are making is not seeing that there is a time delay lag in the digital signal - this causes you to believe that the noise is mainly related to the input signal - try aligning the digital version of the signal with the analogue signal and you will find a point where there is very little relationship between Q-noise and original input (time shifted). 

It's not wrong to do this, after all does a piece of music transmitted from a digital radio station sound any worse after the several hundreds of micro seconds delay between transmission and reception on your digital radio in your kitchen?

You should be looking at it like this: -



And not like this: -



You should be able to see that if you moved the phase of the originating sinewave slightly all artifacts of the input signal are removed: -



Pictures stolen from here and here