In reality only the white portion of the root was located below ground. The purple colored portion was above ground and exposed to the sun, thus the purple pigment. No digging is necessary for sheep to consume roots. When sheep first enter a turnip field and are first exposed to grazing turnips, the turnip is not their first preference. Generally the flock cleans up all of the grass and weeds first and then progress to the turnips.
Most sheep eat the leafy tops first and then move on to consume the root portion.
The roots are usually consumed much as you or I would eat and apple. Sheep that have never been offered turnips before may take several days to become interested and then the feasting takes off. As grazing continues, the sheep appear to prefer turnips roots still attached to the ground to those detached and laying on the surface. Variety preference may also exist. This is due to the high water content of both the root and leaf portions.