We present detailed photo+collisional ionization models and kinematic models of the multiphase absorbing gas, detected within the Hubble Space Telescope(HST)/COS, HST/STIS and Keck/HIRES spectra of the background quasar TON 153 at 104 kpc along the projected minor axis of a star-forming spiral galaxy (z = 0.6610). Complementary g′r′i′Ks photometry and stellar population models indicate that the host galaxy is dominated by an ∼4 Gyr stellar population with slightly greater than solar metallicity and has an estimated log M* = 11 and a log Mvir = 13. Photoionization models of the low-ionization absorption (Mg i, Si ii, Mg ii and C iii), which trace the bulk of hydrogen, constrain the multicomponent gas to be cold (log T = 3.8–5.2) and metal poor (). A lagging halo model reproduces the low-ionization absorption kinematics, suggesting gas coupled to the disc angular momentum, consistent with cold accretion mode material in simulations. The C iv and O vi absorption is best modelled in a separate collisionally ionized metal-poor (−2.50 ≤ [X/H] ≤ −1.93) warm phase with log T = 5.3. Although their kinematics are consistent with a wind model, given the 2–2.5 dex difference between the galaxy stellar metallicity and the absorption metallicity we indicate that the gas cannot arise from galactic winds. We discuss and conclude that although the quasar sightline passes along the galaxy minor axis at a projected distance of 0.3 virial radii, well inside its virial shock radius, the combination of the relative kinematics, temperatures and relative metallicities indicates that the multiphase absorbing gas arises from cold accretion around this massive galaxy. Our results appear to contradict recent interpretations that absorption probing the projected minor axis of a galaxy is sampling winds.