The problem with SW Explorer is that it is not intended to copy the entire project. When you copy an assembly or drawing, you get the option to "Copy children". The key word here is "children", not "all associated files".
When you copy an assembly, all parts and sub-ass'ys are it's children. The drawings of those parts and subs are separate parents to those files than the main assembly (think step-parents). That's why they do not get copied.