Vague is a harsh word. Non-specific is more like it. Article 314 says "rigidly and securely fastened in place." It says little about how that is accomplished as long as your fasteners don't protrude more than 1/4" inside the box.

The extra stuff for ceiling fan boxes (that support the fan) has to be marked as being able to support a weight at least as much as the fan. If the box has any specific mounting requirements, then you are obliged to follow those.

Your AHJ may have specific requirements that they chose to look for, but I've never seen one that get bent out of shape over powder-actuated fasteners vs. tapcons or the like. Nails are OK in shear, I wouldn't (even if it were allwoed) use them to support a box in tension.