For over 30 years, a $\sim 20\%$ deficit, now exceeding $5\sigma$, has persisted between measured and predicted neutrino capture rates on ${}^{71}\mathrm{Ga}$, as observed in radioactive source experiments (namely GALLEX, SAGE, and more recently BEST) using ${}^{51}\mathrm{Cr}$ and ${}^{37}\mathrm{Ar}$. This long-standing discrepancy, referred to as the gallium anomaly, has posed a significant challenge to our understanding of both experimental methods and theoretical predictions. In this Letter, we revisit the theoretical calculation of the neutrino capture cross section by moving beyond the standard treatment of the leptonic wave functions, revealing limitations in the commonly used factorization approach based on the detailed balance principle. Incorporating phenomenologically constrained Gamow-Teller transition densities, able to correctly reproduce the precisely measured half-life of ${}^{71}\mathrm{Ge}$, we find that the revised cross section can be significantly reduced, potentially resolving the gallium anomaly without invoking new physics.