Stellar activity may induce Doppler variability at the level of a few m s(-1) which can then be confused by the Doppler signal of an exoplanet orbiting the star. To first order, linear correlations between radial velocity measurements and activity indices have been proposed to account for any such correlation. The likely presence of two super-Earths orbiting Kapteyn's star was reported in Anglada-Escude et al., but this claim was recently challenged by Robertson et al., who argued for evidence of a rotation period (143 days) at three times the orbital period of one of the proposed planets (Kapteyn's b, P = 48.6 days) and the existence of strong linear correlations between its Doppler signal and activity data. By re-analyzing the data using global statistics and model comparison, we show that such a claim is incorrect given that (1) the choice of a rotation period at 143 days is unjustified, and (2) the presence of linear correlations is not supported by the data. We conclude that the radial velocity signals of Kapteyn's star remain more simply explained by the presence of two super-Earth candidates orbiting it. We note that analysis of time series of activity indices must be executed with the same care as Doppler time series. We also advocate for the use of global optimization procedures and objective arguments, instead of claims based on residual analyses which are prone to biases and incorrect interpretations.