Haha, you used a difference-blend on separate screenshots, didn't you! Nice trick ;)
Not exactly how you put it, but yes, you got the idea right. I had only the black color copied from a few screenshots and stacked the copies all over. Learned this trick back in 2007 on that old static game. Doesn't work with moving objects though, but "impossible to screenshot" is quite an exagerration at this point. A moving background would make it harder to pull off, but with it being merely "static" statics there's even more - inverting colors in a half of shots and stacking the white only can effectively de-noise the background, leaving only the noisy objects. 
Making a few copies like this and extracting the black color again to stack it all over the place will make these objects more opaque, but with a clean background this time. I suddenly felt apathetic so I shaln't bother with making the further example, may I?
Well, I think "'impossible to screenshot' is quite an exaggeration" is an exaggeration, since you're essentially moving the goalposts to "cannot screenshot directly, but can combine data from multiple screenshots into readable picture". That aside, this could be neatly countered by what you suggested with moving background or making the static on the objects move only when the view itself moves (moving the character or the view).
That depends if we debate methods or results. I can't screenshot it, yet i can produce some pretty accurate and recognizeable screenshots here and there without changing a single pixel, which is still technically screenshooting. The same way a long exposure photography is still a photography, albeit it won't capture the instance of a moment. Considering there was no "cannot screenshot directly" condition stated as well - the goalposts are vague enough to stand where they are to be met with my efforts. The pictures I made can be used in a game magazine or in a walkthrough guide as an actual screenshots.
As for countering - you apparently have missed "...at this point" part. I am pretty aware the chaos can be toned up beyond my skill of capturing the shapes inside.