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Given the anisotropic emission from quasar accretion discs, their viewing angle affects estimates of the quasar luminosity, black hole mass, and Eddington ratio. Discs appear overluminous when viewed pole-on and underluminous when viewed at high inclination. In radio-quiet quasars, the viewing angle is usually unknown, although spectroscopic indicators have been proposed. Here, we use a recently discovered universality in the variability structure function (SF) of quasar light curves (LCs), where all quasars show the same SF when clocks run in units of orbital time-scale. As an offset from the mean relation can be caused by incorrect orbital time-scales and thus incorrect luminosities, we correlate these offsets with suggested inclination indicators. We derive SFs from NASA/Asteroid Terrestrial-impact Last Alert System (ATLAS) LCs spanning ∼6 yr of observation, using a sample of 183 luminous quasars with measured H β lines as well as 753 quasars with C  iv and Mg  ii lines. Starting from the proposed orientation indicators, we expect quasars with narrower H β lines and with more blueshifted C  iv lines to be viewed more pole-on and thus appear overluminous. In contrast, our SF analysis finds that presumed pole-on discs appear underluminous, consistently for both line indicators. We discuss possible explanations for the behaviour of quasars with highly blueshifted C  iv lines irrespective of inclination angle, including dusty outflows that might render the accretion disc underluminous and flatter disc temperature profiles with longer orbital time-scales than in thin-disc models but reach no satisfying conclusion. [ABSTRACT FROM AUTHOR]