Rasterize uses default stylesheet if ImageSize is specified

In Mathematica 8.0.4 Rasterize[p] uses the default styles even without ImageSize:

$Version

SetOptions[EvaluationNotebook[], 
  StyleDefinitions -> 
   Notebook[{Cell[StyleData[StyleDefinitions -> "Default.nb"]], 
     Cell[StyleData["GraphicsLabel"], FontColor -> RGBColor[0, 1, 0], FontWeight -> Bold, 
      FontSize -> 16]}, StyleDefinitions -> "PrivateStylesheetFormatting.nb"]];

"8.0 for Microsoft Windows (64-bit) (October 7, 2011)"

p = Plot[x, {x, 0, 1}];
Rasterize[p]

Surprisingly, if we simply wrap Graphics by Style the Notebook's stylesheet is applied (wrapping by Pane, Text or Row also work):

 {Rasterize[Style[p]], Rasterize[Style[p], ImageSize -> 360]}

Unfortunately specifying the stylesheet via Style doesn't work (checked with versions 8.0.4 and 11.0.1):

SetOptions[EvaluationNotebook[], StyleDefinitions -> Inherited]
Rasterize[Style[p, 
  StyleDefinitions -> 
   Notebook[{Cell[StyleData[StyleDefinitions -> "Default.nb"]], 
     Cell[StyleData["GraphicsLabel"], FontColor -> RGBColor[0, 1, 0], FontWeight -> Bold, 
      FontSize -> 16]}, StyleDefinitions -> "PrivateStylesheetFormatting.nb"]]]

But we can specify it as an option of Notebook expression:

Rasterize[Notebook[{Cell[BoxData@ToBoxes@p, "Output"]}, 
  StyleDefinitions -> 
   Notebook[{Cell[StyleData[StyleDefinitions -> "Default.nb"]], 
     Cell[StyleData["GraphicsLabel"], FontColor -> RGBColor[1, 0, 0], FontWeight -> Bold, 
      FontSize -> 16]}, StyleDefinitions -> "PrivateStylesheetFormatting.nb"]]]

With Mathematica version 9.0.1 I can get the result I wanted by specifying the ImageSize as a Graphics option, e.g. using Show, rather than using it as an option to Rasterize:

Rasterize[Show[p, ImageSize -> 200]]

Note that the labels are still at the size specified in the style sheet.

Interestingly, the custom style is used if the graphic is embedded in a non-graphical construct, but in this case the font is demagnified. The following all produce the same output:

Rasterize[Style[p, {}], ImageSize -> 200]
Rasterize[Magnify[p, 1], ImageSize -> 200]
Rasterize[Text[p], ImageSize -> 200]

This is consistent with the documentation for Rasterize (the first two items under the "Properties and Relations" section) which states:

Rasterizing a graphic with a custom ImageSize option works by changing the graphic's ImageSize, not by magnifying the graphic. A graphic embedded in a non-graphical construct will magnify instead.