In the PMNS matrix, the relation $|U_{\mu i}| = |U_{\tau i}|$ (with $i=1,2,3$) is experimentally favored at the present stage. The possible implications of this relation on some hidden flavor symmetry has attracted a lot of interest in the neutrino community. In this paper and the paper Universe 10(1) (2024) 50, we analyse the implications of $|U_{\mu i}| = |U_{\tau i}|$ (with $i=1,2,3$) in the context of the canonical seesaw mechanism. We also show that the minimal symmetry proposed in JHEP 06 (2022) 034 is a possible but not necessary reason for the above-mentioned relation.