The Desktop (including the Bitmap on it) is actually drawn by the window system itself. So that is basically quite deep and old, too. So according to the changes that happened since NT4 I suppose that the painting is actually done in win32k.sys . The driver was created to replace win32.dll which would have done everything in user-mode with context switching.
This said, it goes conform with what erykson commented to your question: win32k!xxxInternalPaintDesktop is the bad guy.
However it should be possible to acquire the DC of the Desktop HWND (0 afaik) and attach it to your own drawing. Not sure if you can turn it into a DirectX DC but this is up to you to try.
BTW. It is possible to re-parent and to capture foreign windows (HWNDs) and associated device contexts (DCs). However you might need to be privileged or an administrator. (security checked)