While I believe that, it’s an issue with the training data, and not the hardest to resolve
So is the example with the dogs/wolves and the example in the OP.
As to how hard to resolve, the dog/wolves one might be quite difficult, but for the example in the OP, it wouldn’t be hard to feed in all images (during training) with randomly chosen backgrounds to remove the model’s ability to draw any conclusions based on background.
However this would probably unearth the next issue. The one where the human graders, who were probably used to create the original training dataset, have their own biases based on race, gender, appearance, etc. This doesn’t even necessarily mean that they were racist/sexist/etc, just that they struggle to detect certain emotions in certain groups of people. The model would then replicate those issues.
Maybe not the hardest, but still challenging. Unknown biases in training data are a challenge in any experimental design. Opaque ML frequently makes them more challenging to discover.
The unknown biases issue has no real solution. In this same example if instead of something simple like snow in the background, it turned out that the photographs of wolves were taken using zoom lenses (since photogs don’t want to get near wild animals) while the dog photos were closeup and the ML was really just training to recognize subtle photographic artifacts caused by the zoom lenses, this would be extremely difficult to detect let alone prove.