In many psychological questionnaires the need to analyze empirical data raises the fundamental problem of possible fake or fraudulent observations in the data. This aspect is particularly relevant for researchers working on sensitive topics such as, for example, risky sexual behaviors and drug addictions. Our contribution presents a new probabilistic approach, called Sample Generation by Replacement (SGR), to address the problem of evaluating the sensitivity of 8 commonly used SEM-based fit indices (Goodness of Fit Index, GFI; Adjusted Goodness of Fit Index, AGFI; Expected Cross Validation Index, ECVI; Standardized Root-Mean-Square Residual Index, SRMR; Root-Mean-Square Error of Approximation, RMSEA; Comparative Fit Index, CFI; Nonnormed Fit Index, NNFI; and Normed Fit Index, NFI) to fake-good ordinal data. We used SGR to perform a simulation study involving 3 different SEM models, 2 sample size conditions, and 2 estimation methods: maximum likelihood (ML) and weighted least squares (WLS). Our results show that the incremental fit indices (CFI, NNFI, and NFI) are clearly more sensitive to fake perturbation than the absolute fit indices (GFI, AGFI, and ECVI). Overall, NFI turned out to be the best and most reliable fit index. We also applied SGR to real behavioral data on (non)compliance in liver transplant patients. (Contains 6 figures and 6 tables.)