Not quite. You don't have to flatten the image, you just have to deselect the pixels you have selected from pasting in the screenshot. Hit Ctrl+D. Or, potentially, you're working on a layer that is covered up by the screenshot. Take a look and make sure the layer you're trying to draw upon is at the top.
Paint.NET, like other image editors, only affects the pixels within the selection area on the selected layer. This doesn't violate Principle of Least Surprise, as it's standard for all image editors.