This is what I got from it:
JK tracks at 96kHz because it captures the tape bandwidth with more fidelity and mixes at 48kHz because he finds his analog gear reacts better to a rolled off 48KHz signal. His point was that tape naturally and gradually rolls off the high frequencies and digital doesn't. His argument was that all this analog gear was manufactured in the Tape Era to work with tape and how tape behaved. Digital captures all frequencies linearly (up to the Anti-Aliasing filter), so in the case of mixing with 96kHz files, you get a lot of "clean" high frequency information up to 48khz, where as in tape it would be heavily rolling off the highs long before that point, thus when mixing with 96kHz digital files, then gear is "over reacting" to all this high frequency information that it's "not accustomed" to "dealing with"!!! Contrarily, mixing at 48kHz with the Anti-Aliasing filter at 24kHz, it behaves "more like tape" with less high frequency information with a high amplitude!!! That's what I understood anyway
EDIT:
Here is a 60 minute talk with Mr. Neve where he gets into his experience with sound, hearing and feeling. This link will jump to 35minutes where he gets into it a bit, but you really owe it to yourself to watch the whole interview. He talks about his 60+ years of experience in the audio industry. It's quite simply brilliant:
http://youtu.be/AGt0KXW_T1Y?t=34m53s
Here's another good spot about frequencies we can't hear, but feel:
http://youtu.be/AGt0KXW_T1Y?t=44m31s