I was able to reproduce the double white border unwanted visual appearance you mentioned. However this doesn't relate to RadExpander. If you create a GroupBox outside RadExpander's Content and add dark background to the container that holds the GroupBox control you'll observe the same visual appearance.
So what can you do to get rid of it -- remove the BorderThickness setting of your GroupBox as the white Borders are TemplateBound to it in the ControlTemplate. Still if you want to see the Black Border and remove the White Borders around the GroupBox you'll have to retemplate the default ControlTemplate.
Even though GroupBox is a MS control, you might still check our help article to see how to edit the control template of GroupBox via Expression Blend or VisualStudio Designer.
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