You are correct, In-Browser Editing does not currently support editing fill or background images.
There are some cases where having a placed image with effects applied (e.g. rounded corners) will still allow In-Browser Editing to replace the image and keep the effects intact. For example: I placed the Muse logo on a page, set two rounded corners, and applied a 1px red stroke. When I preview, I can click/drag the image and see that the image itself is not rounded.
When I apply an inner glow to the image, all the effects are merged down into the image itself.
This is done because not all browsers support the effects and your design might suffer. Muse chooses to rasterize the image instead of relying on HTML/CSS for the effects. In-Browser Editing doesn't know about those effects and won't be able to apply them to new images that are uploaded.
As far as keeping the effects in place, but swapping out the image during design time in Muse, this can be done. Right click on the image and choose "Replace Image...". This keeps the effects applied to the image frame and replaces the image itself.