Surely the reason why training flights cannot take place at a private/unlicensed strip is to prevent students being exposed to marginal airfield environments.
Once qualified they can do what ever they like.
As for the instructor taking over for the landing, you are still exposing your student to possible dangers they may be unaware of.
When you go airside you have a duty of care based on your greater experience of what dangers may exist.
Flying is about reducing risk and covering your ASS!.