Gravitational lens flux-ratio anomalies provide a powerful technique for measuring dark matter substructure in distant galaxies. However, before using these flux-ratio anomalies to test galaxy formation models, it is imperative to ascertain that the given anomalies are indeed due to the presence of dark matter substructure and not due to some other component of the lensing galaxy halo or to propagation effects. Here we present the case of CLASS B1555+375, which has a strong radio-wavelength flux-ratio anomaly. Our high-resolution near-infrared Keck II adaptive optics imaging and archival Hubble Space Telescope data reveal the lensing galaxy in this system to have a clear edge-on disc component that crosses directly over the pair of images that exhibit the flux-ratio anomaly. We find that simple models that include the disc can reproduce the cm-wavelength flux-ratio anomaly without requiring additional dark matter substructure. Although further studies are required, our results suggest the assumption that all flux-ratio anomalies are due to a population of dark matter sub-haloes may be incorrect, and analyses that do not account for the full complexity of the lens macro-model may overestimate the substructure mass fraction in massive lensing galaxies.