Based on 4 yr AMS-02 antiproton data, we present bounds on the dark matter (DM) annihilation cross section vs. mass for some representative final state channels. We use recent cosmic-ray propagation models, a realistic treatment of experimental and theoretical errors, and an updated calculation of input antiproton spectra based on a recent release of the PYTHIA code. We find that reported hints of a DM signal are statistically insignificant; an adequate treatment of errors is crucial for credible conclusions. Antiproton bounds on DM annihilation are among the most stringent ones, probing thermal DM up to the TeV scale. The dependence of the bounds upon propagation models and the DM halo profile is also quantified. A preliminary estimate reaches similar conclusions when applied to the 7 years AMS-02 dataset, but also suggests extra caution as for possible future claims of DM excesses.