We present a detailed exploration of the stellar mass versus gas-phase metallicity relation (MZR) using integral field spectroscopy data obtained from ~1000 galaxies observed by the SAMI galaxy survey. These spatially resolved spectroscopic data allow us to determine the metallicity within the same physical scale (R_eff_) for different calibrators. The shape of the MZ relations is very similar between the different calibrators, while there are large offsets in the absolute values of the abundances. We confirm our previous results derived using the spatially resolved data provided by the CALIFA and MaNGA surveys: (1) we do not find any significant secondary relation of the MZR with either the star formation rate (SFR) or the specific SFR (SFR/M_) for any of the calibrators used in this study, based on the analysis of the individual residuals; (2) if there is a dependence with the SFR, it is weaker than the reported one (r_c~-0.3), it is confined to the low-mass regime (M_<10^9^M{sun}_) or high-SFR regimes, and it does not produce any significant improvement in the description of the average population of galaxies. The apparent disagreement with published results based on single-fibre spectroscopic data could be due to (i) the interpretation of the secondary relation itself; (ii) the lower number of objects sampled at the low-mass regime by the current study; or (iii) the presence of extreme star-forming galaxies that drive the secondary relation in previous results.