Thanks for asking here, John.
Yes, that is the rule. Except for that Trail Crest exit permit, all permits and quotas are strictly for date of entry. With a single permit for entering on a specific date, you get to stay in the back country up to 14 days. So if you have an overnight reservation from the lottery for the MMWT (Main Mt Whitney Trail), you can come out the next day or after two weeks -- the permit people will not make an issue out of it. They ask when you are coming out, and where (approximately) you plan on camping for record-keeping purposes, and to get an idea where to look if you are reported missing.
And then there is also the issue of the PCT hikers. They get an even better deal. They get an almost free pass for their entire journey. They can leave the trail and re-enter, even days later, as long as they have that PCT pass. I believe the PCT association requires that if they are exiting the MMWT, they are required to pay the $15 Whitney Zone fee, and get a stamp on the permit. But then they could head out for a resupply, maybe even a layover, and then head up the Whitney trail without the reservation and permit from the IAVC in Lone Pine.
And now that I go searching, I can't find the specific place of the 14-day rule, but I am sure that it is in place. But it is there to prevent someone from going in and squatting all summer in a single camp and exiting just to resupply, returning and spending every night in the wilderness. I think there is a 14-day campground site rule, too. You can be sure they permit JMT/PCT hikers who enter at Whitney Portal, who may be spending more than 14 days on the trail. But those people are traveling, not squatting in a single place.
