I think his idea is that some non planar wave within the ear would mean that the wavefronts would not be exactly matched for all reflection paths to and within the cochlea. This would mean the phase would not remain as they travel through the cochlea and could construct at some point around the hair cells.

But, considering the wavelength of 20kHz is 1cm and the ear canal is about 0.7, I can't imagine there's much room for anything but a nice planar wave heading down the canal, let alone within the cochlea.