In epithelial cells, planar polarization of subapical microtubule networks is thought to be important for both breaking cellular symmetry and maintaining the resulting cellular polarity. Studies in the Drosophila pupal wing and other tissues have suggested two alternative mechanisms for specifying network polarity. On one hand, mechanical strain and/or cell shape have been implicated as key determinants; on the other hand, the Fat-Dachsous planar polarity pathway has been suggested to be the primary polarizing cue. Using quantitative image analysis in the pupal wing, we reassess these models. We found that cell shape was a strong predictor of microtubule organization in the developing wing epithelium. Conversely, Fat-Dachsous polarity cues do not play any direct role in the organization of the subapical microtubule network, despite being able to weakly recruit the microtubule minus-end capping protein Patronin to cell boundaries. We conclude that any effect of Fat-Dachsous on microtubule polarity is likely to be indirect, via their known ability to regulate cell shape.