We study the compatibility of Alpha Magnetic Spectrometer (AMS-02) data on the cosmic-ray (CR) positron fraction with data on the CR electron and positron spectra provided by PAMELA and Fermi LAT. We do that in terms of a novel propagation model in which sources are distributed in spiral arm patterns in agreement with astrophysical observations. While former interpretations assumed an unrealistically steep injection spectrum for astrophysical background electrons, the enhanced energy losses experienced by CR leptons due to the larger average source distance from Earth allow us to reproduce the data with harder injection spectra as expected in a shock acceleration scenario. Moreover, we show that in this approach, and accounting for AMS-02 results, the contribution of nearby accelerators to the fluxes at very high energy can be significantly reduced, thus avoiding any tension with anisotropy upper limits.