What do graphs of signal vs background neural network outputs represent?

Okay, your output makes sense, given what you wrote in the comments. But if you don't know where the other output comes from, all else is speculation. It could be that it was generated by a neural network with two sigmoid outputs, rather then softmax, and the classification was done based on which output was larger. In that case you are not guaranteed symmetric graphs. So the asymmetric graph does not necessarily imply that it's not generated by a neural network, only that the output does not come from a two-dimensional softmax or a pair of sigmoid/1-sigmoid.