In his award-winning contribution to the biannual PSA conference at Pittsburgh in 2008, Christian Wüthrich mounted an argument against structuralism about spacetime in the context of the general theory of relativity (GTR), to the effect that structuralists cannot discern space-time points: an "abysmal embarrassment" for the structuralist, Wüthrich judged. Wüthrich's characterization of space-time structuralism is however incorrect. We demonstrate how, on the basis of a correct characterization of space-time structuralism, it is possible to discern space-time points in the GTR structures under consideration. Thus Wüthrich's argument crumbles.