The 12 meter stop is not in the instructor manual for the course. It does discuss the old Navy omitted decompression procedure of descending back down to 12 meters but this is no longer recommend.
...which is why I had never heard of this until I saw this thread, even though I have certified a fair number of people in this specialty. What follows is some speculation coupled with recent research I have done.
When the course was written, deep stops were all the rage. many people were swearing by them, even though there was very little research to support it. There was, however,
some research, some of which has since fallen out of favor. At about that time, NAUI made deep stops on recreational dives part of its instruction, and it is still part of NAUI's instruction.
Previous posters have noted that the love affair of deep stops in technical diving is clearly over. So what about deep stops on recreational dives? Well, it is complicated.
My research on recreational deep stops has made it clear to me that although all dives require decompression, there is a difference between NDL dives and decompression dives, with a gray area of transition at the limits of NDL dives and decompression dives requiring minimum decompression. Think about it this way. If you go into decompression and begin an ascent, a dive computer will penalize you for ascending too slowly, forcing you to do longer and deeper decompression stops. If you do
not go into decompression and ascend slowly, that same computer will reward you by giving you more NDL time, usually without changing a safety stop requirement. You could potentially be near NDL at depth and then do a 20 minute extension of your dive at a shallower depth without a problem. You will only be penalized if your slow ascent exceeds NDL limits.
There is still very little research on deep stops in recreational diving. I was planning on writing an article about current thinking on the topic, but after researching, I decided I did not have enough of an opinion to write it. In contrast, I have firm opinions on deep stops in decompression diving.
Today, NAUI remains the only agency I know of that truly endorses deep stops on recreational dives. DAN Europe endorses them, but DAN America does not.