If there are sheep on the land then the CPH will be being used, quite properly, for the movements on and off that land. Having a CPH does not mean the holder of the CPH owns sheep, nor does it necessarily mean they control the land. (You can hold a CPH for land that someone else owns.)
Sorry, I know it is complex. The best thing, I think, would be to keep it simple and say that the owner of the land appears to be letting the grazing, does not own their own sheep, and therefore cannot be said to be farming it themselves.