  We present new VLT/X-Shooter optical and NIR spectra of a sample of 17
candidate young low-mass stars and BDs in the rho-Ophiucus cluster. We derived
SpT and Av for all the targets, and then we determined their physical
parameters. All the objects but one have M*<0.6 Msun, and 8 have mass below or
close to the hydrogen-burning limit. Using the intensity of various emission
lines present in their spectra, we determined the Lacc and Macc 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 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 Macc with M* when comparing low-mass stars and BDs.
Moreover, we find a similar small (1 dex) scatter in the Macc-M* relation as in
some of our recent works in other star-forming regions, and no significant
differences in Macc 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 Macc-M* correlation confirms
that Macc in the literature based on uncertain photospheric parameters and
single accretion indicators, such as the Ha 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.
