According to the website, one does not even have to be certified to dive to sign up for this internship. But materials ARE supposed to be included.
PADI has some control over what is done in their name, to the extent that standards violations can result in termination of instructor status, or get a dive shop kicked out of the 5 star program. But if the shop is doing something which is not sold using any PADI umbrella, they can do whatever they want. They would be in interesting liability trouble, were a problem to occur, but as has already been pointed out, this is happening in Mexico, where the liability situation is very different from the US -- and I would guess that a lot if not all of the "pseudo-Discover Scuba" students are from other countries, where filing a lawsuit in Mexico would be a major, expensive PITA.
I personally believe it is inadvisable for staff with no teaching training or experience to be conducting introductions to scuba, and I also think anybody who is even in a pool with someone on their first experience breathing underwater should, at the very least, have a great deal of composure in the water themselves. This is not often the case for simple OW divers with low dive counts.
