Yes dhadley, in my experience that's consistent behaviour for Civil 3D: the "Independent layer on" variable only applies to the
Layer On/Off status; perhaps what is needed is a "Independent layer thawed" variable.
To get around it, I've set up my points so that the points I want invisible go to a point group "Points - invisible" point group,
which is on a "Points - invisible" layer (which is also a non-plot layer), the ones I want visible go to their respective service
point group (on their respective service layer) or to a "Visible points" point group which is on a "Points - visible" layer. The
description key combined with the inclusion criteria of the point groups does the majority of the distribution. That way, my primary
display control is via point groups and layers rather than styles and the "Independent layer on" variable doesn't really come into
the equation. Yes, a couple more layers to clutter the Layer Manager, but only a couple and ones that have proven completely
justifiable.
Hope that helps,
Trevor