AzAtty once bubbled...
...there are several lawyers on the board. I'm one of them.
29 CFR 1910.401(a)(2)(i) states that the regulations propounded by OSHA governing commercial diving operations do not apply to "any diving operation: (i) Performed solely for instructional purposes, using open-circuit, compressed-air SCUBA and conducted within the no-decompression limits." I haven't researched the annotations to that section, but it appears that recreational scuba instruction could fall within that exception. On further consideration, though, scuba instruction may still be subject to the regulations. I'll have to do some more research on the topic.
29 CFR 1910.426 governs "mixed-gas diving." That section says nothing about particular training being necessary to use a mixed gas in commercial diving operations.
I also ran a quick search using the terms "nitrox" and "enriched air" separately on Westlaw using the ALLCASES database. That database covers every reported case in the United States. There were six "hits" on "enriched air" and eight hits on "nitrox." All of them were patent infringement cases. Not a single case involved an OSHA enforcement action or a personal injury case.
There may be other regulations that I did not find. Admittedly, I only spent about ten minutes looking, so you're welcome to do more research if you like.
Now, for my thoughts on radagalf's hypothetical:
I intentionally will not provide what I think is the "right" answer to the question. In my Quantitative Business Analysis course during my MBA program, the professor said on the first day that you cannot judge the quality of the decision based upon the result you get. That's really a profound statement, and it seems counterintuitive. People don't understand it unless they understand how to make decisions. Sometimes very good decisions have bad results, and very bad decisions have good results. The best you can do is analyze the data and information you have available to you, and settle on a course of action.
Analyze the situation yourself: the student will die if he can't breathe, and the student may suffer a toxic episode if he breathes enriched air. In either case you'll get sued, so make the decision that maximizes the chances of the student living and minimizes your chance of being sued. Keep in mind that there are standard emergency responses set by your agency to which you should adhere--at least if you want to be covered by their insurance policy. Following those standards may provide you with defenses to claims brought by the diver. At the same time, you need to know when to bend or break the rules.
Even if you make the "right" decision, you may be held liable on other grounds. How did the student run out of air? Were you down too long? Did you check tank pressure at the beginning of the dive? Did you check the equipment for any leaks? Did you notice any signs of distress or heavier than normal breathing? Did you signal your students to check their air every ten minutes? The list goes on and on.
Ultimately, the issue is whether you acted as a reasonable and prudent instructor would have acted under the circumstances. I can't provide an answer to that question, but you should look at the standards provided by your agency and other agencies. Those are probably the best place to start.