Local vs global
It is hard to imagine why experienced scholars/analysts confuse local analysis with global analysis, say a local robustness analysis with a global robustness analysis. Would they confuse local news with global news? Or local anesthetic with global anesthetic? Or local weather with global weather?
The following narrative outlining the Treasure Hunt problem illustrates the local vs global issue in the context of decision-making under severe uncertainty:
The local robustness analysis in the designated neighborhood is justified if we are confident that the treasure is located in this neighborhood. It is not justified if this is not the case.
The issue is then extremely simple. If the set of possible/plausible values of the parameter of interest, call it A, is very large, and the uncertainty in the true value of this parameter is severe, the proposition to conduct the robustness analysis on a very small neighborhood of A, call it B, rather than on A must be justified. In the above example A represents the island and B represents the small white circle.
The other side of this argument is the following. If you claim to be confident that the true value of the parameter of interest is in the relatively small set B, then you must make a good case to explain why you designate the much larger set A as the set of possible/plausible values of the parameter. Indeed, you must justify your claim that the uncertainty in this case is severe.