First you have to figure out what "damp" means.
Article 100 blurs this
Location, Damp. Locations protected from weather and not subject to saturation with water or other liquids but subject to moderate degrees of moisture. Examples of such locations include partially protected locations under canopies, marquees, roofed open porches, and like locations, and interior locations subject to moderate degrees of moisture, such as some basements, some barns, and some cold-storage warehouses.
Location, Dry. A location not normally subject to dampness or wetness. A location classified as dry may be temporarily subject to dampness or wetness, as in the case of a building under construction.
I think you have to look at the issue. Will the kraft paper in the cable wick up water and deposit in a box?
I don't see a big deal with removing the "3 floor" language as long as they still say type III, IV and V.
The fire rating and sprinklers cover your fire concerns