Does that have to do with how much noise is getting into the amp or what?
No, total harmonic distortion is a property of the waveform you are trying to amplify.
A pure sin wave has no distortion in it. This is of course impossible but it gives the lowest power output because the RMS calculation gives a direct power equivalent output to a DC power of the same value.
Try and think of it as a base level where the RMS voltage to peak voltage relationship you learned about earlier holds.
As the wave shape gets more distorted more energy is fed into the load and at a point of 100% distortion you will output the DC power levels you first calculated and were surprised did not match the data sheet.
For power calculation purposes it is assumed you have a pure undistorted sin wave at one frequency. As the wave gets more complex, it has more harmonics and pushes up the average power.