We have measured the photonic bandstructure of GaAs photonic-crystal waveguides with high resolution in energy as well as in momentum using near-field scanning optical microscopy. Intriguingly, we observe additional bands that are not predicted by eigenmode solvers, as was recently demonstrated by Huisman et al. [Phys. Rev. B 86, 155154 (2012)]. We study the presence of these additional bands by performing measurements of these bands while varying the incident light power, revealing a non-linear power dependence. Here, we demonstrate experimentally and theoretically that the observed additional bands are caused by a waveguide-specific near-field tip effect not previously reported, which can significantly phase-modulate the detected field.