I wrote a test intending to find exactly how points are quantized when figuring the region bounding box, so I can make sure I don't break it. Surprisingly, I'm able to just pass in fractional values and get them back. Clearly this isn't based on any quantization.
MSDN says "The rectangle returned by Region::GetBounds is not always the smallest possible rectangle."
MSDN also says that the world and page transformations of the Graphics object are used, which doesn't seem to be the case, but I choose to selectively believe it when tests agree.
So the rectangle we return must enclose the region, but it may be larger than necessary to enclose the region. This is conveniently exactly the same as the get_region_bounding_box function I wrote earlier. (While there may be implementation differences, I think we can worry about that if/when it becomes a problem. We already got by on something very different from native for a long time.)