We present new VLT/X-Shooter optical and near-infrared spectra of a sample of 17 candidate young low-mass stars and brown dwarfs located in the {rho}-Ophiucus cluster. We derived the spectral type and extinction for all the targets, and then we determined their physical parameters. All the objects but one have M_*_<~0.6M_{sun}_, and eight have mass below or close to the hydrogen-burning limit. Using the intensity of various permitted emission lines present in their spectra, we determined the accretion luminosity and mass accretion rates ({dot}(M)_acc_) for all the objects. When compared with previous works targeting the same sample, we find that, in general, these objects are not as strongly accreting as previously reported, and we suggest that the reason is our more accurate estimate of the photospheric parameters. We also compare our findings with recent works in other slightly older star-forming regions, such as Lupus, to investigate possible differences in the accretion properties, but we find that the accretion properties for our targets have the same dependence on the stellar and substellar parameters as in the other regions. This leads us to conclude that we do not find evidence for a different dependence of {dot}(M)_acc_ with M_*_ when comparing low-mass stars and brown dwarfs. Moreover, we find a similar small (<~1dex) scatter in the {dot}(M)_acc_-M_*_ relation as in some of our recent works in other star-forming regions, and no significant differences in {dot}(M)_acc_ due to different ages or properties of the regions. The latter result suffers, however, from low statistics and sample selection biases in the current studies. The small scatter in the {dot}(M)_acc_-M_*_ correlation confirms that mass accretion rate measurements in the literature based on uncertain photospheric parameters and single accretion indicators, such as the H{alpha} width, can lead to a scatter that is unphysically large. Our studies show that only broadband spectroscopic surveys coupled with a detailed analysis of the photospheric and accretion properties allows us to properly study the evolution of disk accretion rates in star-forming regions.