It appears from the MSDN docs that type DataGridViewAdvancedCellBorderStyle::OutsetDouble can only be used for the right border if the dataGridView is set to RightToLeft processing. If I change the RightToLeft property to True then the border does show correctly as double.
If I set the right style to none and RightToLeft is set to false then the border disappears so it is being set.
Look under the Exceptions section of the docs here.