We analyzed simultaneous archival XMM-Newton and RXTE observations of the X-ray binary and black hole candidate Swift J1753.5-0127. In a previous analysis of the same data a soft thermal component was found in the X-ray spectrum, and the presence of an accretion disk extending close to the innermost stable circular orbit was proposed. This is in contrast with the standard picture in which the accretion disk is truncated at large radii in the low/hard state. We tested a number of spectral models and we found that several of them fit the observed spectra without the need of a soft disk-like component. This result implies that the classical paradigm of a truncated accretion disk in the low/hard state can not be ruled out by these data. We further discovered a broad iron emission line between 6 and 7 keV in these data. From fits to the line profile we found an inner disk radius that ranges between ~6-16 gravitational radii, which can be in fact much larger, up to ~250 gravitational radii, depending on the model used to fit the continuum and the line. We discuss the implications of these results in the context of a fully or partially truncated accretion disk.