If we carefully examine the analysis leading to that conclusion, we will find lurking the assumption that the weighting function used in the least-squares estimation is uniform.
Alternate lines are input and output.
Recall that the inverse to an all-pass filter is its time reverse. The reversed shape of the filter is seen on the inputs where there happen to be isolated spikes. Let us see what theory predicts cannot be done, and then I will tell you how I did it. This takes the autocorrelation of the input and uses it as a gradient search direction. This function vanishes everywhere except for the impulse itself, which is constrained against rescaling.