I would personally prefer a parent to be present, mainly to cover your back - you can get accused of anything now and as a point of safety fot not only you/or instructor other adults in the form of parents is perfect. As if accusations are made wether they be of neglect, abuse etc. etc. having lots of witnesses is very useful.
I would also make a point of having a parent or other adult present during private tuition - I wouldn't dare teach anyone without someone else present. It's just not worth it!!!