The magnetism in the quiet regions of the solar photosphere carries information on the dynamo processes and its interaction with the convection of the outer layers of the sun. Unfortunately, the scales of the magnetic structures on these regions are mostly unresolved. It is therefore instrumental to tell apart the intrinsic field strengths in those regions from the flux through the resolution element. This disentanglement has been far from obvious, leading to opposing views of the magnetic topology in the unresolved structures of the quiet Sun. Our study contributes to the disentanglement of field strength from flux in the quiet Sun, at least, through the use of new observational constrains in the form of spectropolarimetry of Mn i lines observed in the solar spectrum.The chosen Mn lines present a strong coupling with hyperfine structure resulting in spectral features, present or absent as a function of field strength alone. We observe one of those lines simultaneously and co-spatially with the Fe i lines at 630 nm, at the core of the previous measurements.The inversion of the observed Fe lines results in either strong or weak fields depending on the initializations of the inversion algorithm. All the solutions show nevertheless equally good values for the σ parameter and are therefore equally valuable as solutions. The Mn however selects unambiguously strong or weak fields, sometimes agreeing with the inversions of the Fe lines, but half the time disagreeing with them.The Fe i lines at 630 nm, in the conditions found in the quiet Sun, carry no binding information on field strength. A proper analysis of quiet Sun magnetism should necessarily pass through its simultaneous and co-spatial observation with other lines imposing constraints on field strength, as the Mn i lines here analyzed. Ultimately, the magnetic topology of the quiet Sun shall arise from the coherent analysis of all these lines, sensitive to the Zeeman effect.