Nick
I looked into Point Labels and Symbols this morning for you and I see the same behavior. A Point Symbol is just a different way to represent a point in TBC which is why when you click on the symbol that it says it is a point. You can see that Points do not at least expose their Color property - it appears that a point always uses By Layer in TBC as its color, however it seems that when we export that to AutoCAD DWG it always gets written as 255,255,255 which is why they appear white on a black background. 255,255,255 is the default color for the Points layer in TBC, but even if I change that in TBC it still writes the data on that layer with color 255,255,255 which appears incorrect - either it is hard coding point data to be that color or the Points Layer - I think it is hard coding the point data to be white and that would seem to be incorrect - it should be By Layer. I will log this in as a defect.
Alan