Several studies have pointed out an excess in the AMS-02 antiproton spectrum at rigidities of 10-20 GV. Its spectral properties were found to be consistent with a dark-matter particle of mass 50-100 GeV which annihilates hadronically at roughly the thermal rate. In this work, we reinvestigate the antiproton excess including all relevant sources of systematic errors. Most importantly, we perform a realistic estimate of the correlations in the AMS-02 systematic error which could potentially fake a dark-matter signal. The dominant systematics in the relevant rigidity range originate from uncertainties in the cross sections for absorption of cosmic rays within the detector material. For the first time, we calculate their correlations within the full Glauber-Gribov theory of inelastic scattering. The AMS-02 correlations enter our spectral search for dark matter in the form of covariance matrices which we make publicly available for the cosmic-ray community. We find that the global significance of the antiproton excess is reduced to below 1 $sigma$ once all systematics, including the derived AMS-02 error correlations, are taken into account. No significant preference for a dark-matter signal in the AMS-02 antiproton data is found in the mass range 10-10000 GeV.
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