Global fits of cosmic-ray (CR) fluxes measured by AMS-02 provide great potential to search for exotic sources of antimatter such as dark matter (DM). Previous studies of the AMS-02 antiproton data revealed an excess compatible with DM annihilation. In this article we discuss the robustness of this finding studying two sources of systematic uncertainties affecting the result: the production cross sections for secondary antiprotons and possible correlations in the experimental data, so far not provided by AMS-02. While the former has only a mild effect on the significance of the signal (persisting at the $3\sigma$-level), correlations in the data potentially have a strong impact. Using data-driven benchmark models for the correlations, their inclusion can greatly improve the constraining power of the data and, furthermore, enhance the significance of the DM signal up to above $5\sigma$. The analysis reveals the importance of providing the covariance of the experimental data to fully exploit its potential.