We present a detailed exploration of the stellar mass vs. gas-phase metallicity relation ( MZR ) using integral field spectroscopy data obtained from \sim 1000 galaxies observed by the SAMI Galaxy survey . These spatially resolved spectroscopic data allow us to determine the metallicity within the same physical scale ( \mathrm { 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 ) nor 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 } \sim - 0.3 ) , it is confined to the low mass regime ( M _ { * } < 10 ^ { 9 } M _ { \odot } ) or high SFR regimes , and it does not produce any significant improvement in the description of the average population of galaxies . The aparent disagreement with published results based on single fiber 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 .