32-bit Flash player in 64-bit Safari: how?

Question

Yes, I know, WebKit uses a separate 32-bit process to play Flash and communicate with it.

But how does Flash draw in a browser? In Mac OS X you cannot draw on a foreign window or reparent your one.

So if the Flash player hosts in another process, how can it obtain the browser window's context (CGContextRef) and be drawn in it?