We present a controlled rare-weak-link theory of the superfluid-to-Bose/Mott glass transition in one-dimensional disordered systems. The transition has Kosterlitz-Thouless critical properties but may occur at an arbitrary large value of the Luttinger parameter $K$. In contrast to the scenario by Altman {it et al.} [Phys. Rev. B {bf 81}, 174528 (2010)], the hydrodynamic description is valid under the correlation radius and defines criticality via the renormalization of microscopically weak links, along the lines of Kane and Fisher [Phys. Rev. Lett. {bf 68}, 1220 (1992)]. The hallmark of the theory is the relation $K^{(c)}=1/zeta$ between the critical value of the Luttinger parameter at macroscopic scales and the microscopic (irrenormalizable) exponent $zeta$ describing the scaling $propto 1/N^{1-zeta}$ for the strength of the weakest link among the $N/L gg 1$ disorder realizations in a system of fixed mesoscopic size $L$.
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