An overnight permit, as would be required for a more conventional route like Portal-Trail camp-summit-portal is required, since both the MR and MWMT are in the Mount Whitney zone. Might want to wait for Steve to back me up on this.
I'm curious. What is the attraction in descending the MR?
Well, I'm not sure what permit they would need, but I think you're right, an overnight Main Trail permit, since that is the trail they started on. That permit would enable going anywhere else in the Sierra, so coming down the MR would be the same as going elsewhere and spending the night.
As for descending the MR: I think I would opt for the other direction on such a circuit. But then, why not just day hike and do that? If I were carrying overnight gear to the top, I would probably spend the night on the summit (as long as I had some acclimatization, otherwise I'd be miserable up there.) Of course, going the other way around with an overnight permit would require a MR overnight permit, which is harder to get due to the quota of 10, PLUS a Trail Crest exit permit. So maybe that is the reason they chose the MT entry, MR exit.
