Scanning electron microscopy (SEM) is a principal tool for studying nanomaterials, including carbon nanotubes and graphene. Imaging carbon nanomaterials by SEM, however, increases the disorder mode (D-mode) in their Raman spectra. Early studies, which relied on ambiguous ensemble measurements, claimed that the D-mode indicates damage to the specimens by a low-energy electron beam (e-beam). This claim has been accepted by the nanomaterials community for more than a decade without thorough examination. Here we demonstrate that a low-energy e-beam does not damage carbon nanomaterials. By performing measurements on single nanotubes, we independently examined the following factors: (1) the e-beam irradiation itself, (2) the e-beam-deposited hydrocarbon, and (3) the amorphous carbon deposited during synthesis of the material. We concluded that the e-beam-induced D-mode of both carbon nanotubes and graphene originates solely from the irradiated amorphous carbon and not from the e-beam itself or the hydrocarbon. The results of this study should help minimize potential ambiguities for researchers imaging a broad range of nanomaterials by electron microscopy.