Motivated by several claims of spin-orbit-driven spin-liquid physics in hexagonal Ba3Ti3-xIrxO9 hosting Ir2O9 dimers, we report on resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge for different x. We demonstrate that magnetism in Ba3Ti3-xIrxO9 is governed by an unconventional realization of strong disorder, where cation disorder affects the character of the local moments. RIXS interferometry, studying the RIXS intensity over a broad range of transferred momentum q, is ideally suited to assign different excitations to different Ir sites. We find pronounced Ir-Ti site mixing. Both ions are distributed over two crystallographically inequivalent sites, giving rise to a coexistence of quasimolecular singlet states on Ir2O9 dimers and spin-orbit-entangled j=1/2 moments of 5d5Ir4+ ions. RIXS reveals different kinds of strong magnetic couplings for different bonding geometries, highlighting the role of cation disorder for the suppression of long-range magnetic order in this family of compounds
