Speaking as a parent (although I'm a grandfather now, I have a good memory!) may I suggest that the decision should be a mutual one, between you, the child, and the parent? I would strongly suggest, though, that you discourage the parent from being in the same music room as the lesson; it's distracting for the child. On the other hand, I would also strongly suggest that you make some provision for the parent to be at least nearby, if not within earshot.
Why? Well... it may make some parents more comfortable. It may be the only real option for the parent, other than going and sitting in their car (my children's piano teacher lived well out in the country; had she not had a comfortable kitchen, I would have been sitting out in the car for the duration of the lesson -- and, bluntly, would have found another teacher who was more accomodating). It may make some children more comfortable.
One size fits all very rarely works...