I found a method that works on a 0/0/0/100 background (just stumbled into it and it isn't intuitive).
Fill the frame with Paper and the image with Black, then set BOTH the frame and the image to Difference in the Effects panel.
The white frame edge seems to be a display anomaly in ID -- it isn't present inthe PDF I exported -- and even better, I just discovered this seems to work on many other background colors, too (though not all) if you set the image fill to the same color as the background.