Hmmm, wonder how they got permission to do that. I think it is within the Biosphere Reserve. I have a book describing a group making a very similar journey in 1910 via burro. Have to confess it makes me a little disturbed to see wealthy US folk romping through the dunes. That's a real fragile ecosystem. Guess the rich have to challenge themselves somehow.
Within the biosphere reserve there are a few different types of protection going on. There are some trails that you can get permit for but then there are areas which are completely off limits and only researchers are allowed access. They probably have permission for certain areas, I assure you if the go where they are not supposed to it wont be long before they are booted out.