Hi, bit late response to a message from 2015, but I had the same problem. I understand that deleting means 'deleting', but when I move an object, I'd like to move it on the 'paper' (i/e the white background). I use Paint.net for creating and adjusting office plans, so if I move a desk, I'd like to leave white space behind and not go back in and fill it up.
I resolved it by starting with a totally white background layer. But it still takes some playing around to find out what works best for this particular use.
First I started with a basic floor plan and then create alternatives on layers on top. However, it bugged me that with each change I needed to have to go back in and whiten away pieces of the original shining through.
So now I I prefer to copy the original floor plan, rename that into 'Plan date x', make the real original invisible, and then start playing around with new layer.