We show that the electron-phonon coupling strength obtained from the slopes of the electronic energy vs wave vector dispersion relations, as often done in analyzing angle-resolved photoemission data, can differ substantially from the actual electron-phonon coupling strength due to the curvature of the bare electronic bands. This effect becomes particularly important when the Fermi level is close to a van Hove singularity. By performing ab initio calculations on doped graphene, we demonstrate that, while the apparent strength obtained from the slopes of experimental photoemission data is highly anisotropic, the angular dependence of the actual electron-phonon coupling strength in this material is negligible.