Background/Objectives: Clinical scores are recommended for excluding acute appendicitis without imaging, but their rule-out thresholds were derived in patients selected on suspicion of appendicitis. This study tested whether these thresholds retain their reported sensitivity in patients selected by CT performance, estimated the incremental diagnostic value of successive layers of clinical information, and, as an exploratory aim, compared machine learning models with the scores. Methods: This single centre retrospective cohort comprised 761 emergency department patients undergoing abdominal CT for acute abdominal pain. The Alvarado score, the Appendicitis Inflammatory Response (AIR) score and the Adult Appendicitis Score (AAS) were reconstructed from data documented before CT. The reference standard was histopathology in operated patients and the index CT report with the clinical course otherwise. Models were fitted to five cumulative information layers by cross-validation, with nested algorithm selection and a temporal split. Results: Appendicitis was confirmed in 178 patients (23.4%). Sensitivity at the recommended thresholds was 0.680 (95% CI 0.609 to 0.751), 0.848 (0.791 to 0.899) and 0.697 (0.628 to 0.764), against published values of 0.99, 0.95 and 0.959, leaving 57, 27 and 54 confirmed cases in the low probability strata, and the shortfall was present in both temporal periods. Discrimination was preserved, with areas under the curve of 0.848, 0.868 and 0.881. Model discrimination rose from 0.874 with symptoms to 0.918 with laboratory values, with each increment conditional on the preceding layers and the pattern similar with a single algorithm held fixed. With nested selection, the model was not distinguishable from the AAS, and in the later temporal period its deferral threshold attained a sensitivity of 0.925. Conclusions: In a population defined by imaging rather than by clinical suspicion, the recommended rule-out thresholds did not translate. Thresholds should be re-derived and verified in the population in which imaging is to be deferred. The model analysis was exploratory and was not externally validated.