I have never heard of "cooking" a whole steak this way, but there are many other items that use an acid to "cook" food. Usually the food is cut into very small pieces so that the acid can penetrate all the way through. The best example of this is the Latino dish Seviche (Ceviche). Raw seafood is finely diced, and then tossed with numerous different acids though usually it is a citrus juice of some sort. The seafood is left to "cook" in this acid until done (usually 1/2 to 1 hour, though sometimes for a shorter period). It is then tossed with various ingredients ranging from chiles to tomatos, to tropical fruits, depending on the style you are trying to make.
Beef is less often prepared this way, and those that usually are, are tossed just before serving so as to not cook the meat too much. Dishes such as tartare or carpaccio usually have some acid component to them, thus they are tossed at the last minute so that the meat doesn't cook.
As for safety, there is always a risk involved in eating raw meat, be it seafood or beef. I have yet to get sick from any such raw preparation. You just need to take a few precautions.
1. buy from someone you trust and let them know that it is being used for a raw preparation so that you get the freshest available
2. keep all your equipment as cold as possible during preparation and only work with a little of the meat at a time, and cut it into a bowl placed in an ice bath
3. be very careful of cross-contamination. And WASH your hands constantly
4. Eat what you make, don't save it for the next day.
Follow these simple rules and your raw meat preparations should be safe, though once again, there is always a risk eating raw meats. And as one other disclaimer, before I go, pork or chicken tartare is a big NO-NO!!!!!