This is analogous to a person from the early days of photography having no knowledge of the possibility of image doctoring, and us feeling "smug" because a photo like this would elicit confusion.
It seems to me you just have to run your NN on pairs of doctored and undoctored images, and create a separation of concern between scene continuity and object recognition. It's likely that a lot of implementations currently rely too much on surrounding context for successful categorization.
It's also worth exploring certain image analysis techniques during pre-processing to draw out certain attenuated aspects. Edge detection is par for the course, but things like shading are also important to attenuate so that the NN has an easier time learning.
If we're dealing with multiple frames and not just a single image, this opens up a whole dimension of temporal analysis that should make it trivial to separate the background from juxtaposed images.