I do not believe that there will be a legal requirement for minimum depth (like there is for electric cables). There is no danger to humans except perhaps tripping or strangulation.
I was not very impressed with the "workmanship" at my place either. The section between the road and my house was placed on the top of my fence rails (underneath would look better).
Did you ask for them to bury the cable at the scooping visit? If so, what did they say?