This kind of description about negative feedback and how it works is a classic example of thinking over too long a timescale. The comparing of the input with the output and error correction happens continuously at very high speed, from microsecond to microsecond. It is true that negative feedback cannot somehow go back in time and undo something that has already happened, but because the error correction is happening continuously at high speed, the error (or deviation from the true signal) is never allowed to get very large before it is corrected. The more powerful the feedback, and the faster it is, the smaller the deviations from the signal are, and hence the lower the distortion. The small deviations or wobbles of the output signal caused by the feedback applying continuous high speed minor corrections to bring the signal back on track form a high frequency harmonic superimposed on the signal - e.g. added harmonic distortion. However, this very low level distortion is traded off against the much larger harmonic distortion, caused by the inherent non linearity of the active devices, that would have existed had negative feedback not been in operation.
(A good analogy would be steering a car down a straight road. The car will continually move slightly off course, but the driver will notice very early any deviation and apply correction via the steering wheel. The car will not follow a perfect straight line, but if the drive responds rapidly and accurately, deviations are kept to a minimum. The faster the driver responds, the smaller are the actual deviations). Negative feedback can never bring distortion down to zero, but if it is fast enough and powerful enough, it can get very close.
I have yet to come across any other technique that can get so close, e.g. distortion levels of 0.000015% typical of high end op amps, or 0.001% and better achieved by Douglas Self's "Blameless" power amp designs.
