Exposed rock is typically appearing on mountainous trails.
For surface of small crushed rock fragments surface=gravel will be more fitting.
Areas of exposed bedrock are tagged with natural=bare_rock.
Processed natural stone can be used to create surface=unhewn_cobblestone, surface=sett and surface=paving_stones surfaces.
Note that surface=rock is applicable both in some cases of man-made surfaces of trails and in cases where trail goes across exposed bare rock.
Natural rock, with nearly no processing used to pave a mountainous path. The best tagging of that is likely highway=steps + surface=rock
Natural rock, with nearly no processing used to pave a mountainous path. Probably best tagged as highway=path surface=rock
Rock covered trail surface on the Ole Ranger Trail at Patapsco Valley State Park