Please follow those steps:
CurrentValue[EvaluationNotebook[], ScreenStyleEnvironment] = "SlideShow"
SetOptions[
EvaluationNotebook[],
StyleDefinitions -> Notebook[{
Cell[StyleData["Notebook"],
DockedCells -> {Inherited, Inherited, Cell[TextData["TEST"]]}]
},
StyleDefinitions -> "Reference.nb"
]]

As you can see, those double slideshow toolbars are inherited from somewhere even though there is no reference to Core/Default in StyleDefinitions.
Where are they from?
Cell[StyleData[All, "SlideShow", StyleDefinitions -> StyleData[All, "Presentation"]], PageWidth->WindowWidth, DockedCells->FEPrivate`FrontEndResource["FEExpressions", "SlideshowToolbar"], ScrollingOptions->{"PagewiseDisplay"->True, "VerticalScrollRange"->Fit}, ShowGroupOpener->False, MenuSortingValue->1300]– Mike Honeychurch Jun 29 '15 at 23:58FEPrivateFrontEndResource["FEExpressions", "SlideshowToolbar"]) for slideshows. So for me this does what is expected. – Mike Honeychurch Jun 30 '15 at 07:39