  We show that the anisotropy of the effective spin model for the dimer Mott
insulator phase of $\kappa$-(BEDT-TTF)$_2X$ salts is dramatically different
from that of the underlying tight-binding model. Intra-dimer quantum
interference results in a model of coupled spin chains, where frustrated
interchain interactions suppress long-range magnetic order. Thus, we argue, the
"spin liquid" phase observed in some of these materials is a remnant of the
Tomonaga-Luttinger physics of a single chain. This is consistent with previous
experiments and resolves some outstanding puzzles. An erratum [Phys. Rev. Lett.
120, 199901 (2018).] is added as an appendix.
