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We conduct high-accuracy calculations of isotope shift (IS) factors of the states involving the D_{1} and D_{2} lines in Zn II. Together with a global fit to the available optical IS data, we extract nuclear-model independent, precise differential radii for a long chain of Zn isotopes. These radii are compared with the ones inferred from muonic x-ray measurements. Some deviations are found, which we ascribe to the deformed nature of Zn nuclei that introduces nuclear-model dependency into radii extractions from muonic atoms. We arrive at the conclusion that, in cases where the many-body atomic calculations of IS factors are well established, optical determinations of differential radii are more reliable than those from the muonic x-ray measurements, opening the door to obtaining more trustworthy nuclear radii across the nuclear chart.