Researchers can specify more or less input output than the details of the study. There will be no difference in scores. 

The main point made by Simar and Wilson is that a two-stage DEA approach makes sense only if there is separability between the two stages. I agree that testing this is difficult, but at least some kind of exogeneity should be argued for the variables included at the second stage. They should be environmental variables which not only can potentially affect the efficiency but also are characterised by some kind of exogeneity regarding the first stage.