  We introduce the notion of a Bayesian analysis motivated `reliability' that
gives a truer distinction of cusp-core and other halo-parameters (like
mass-concentration) in an ensemble of observed galaxies. Our approach goes
beyond the standard statistical techniques of parameter estimation and model
fitting. We create hundreds of thousands of realistic mock SPARC RCs, with both
cuspy and cored DM density profiles as model inputs. These RCs carefully
incorporate the details of SPARC data such as the nature of observed
uncertainties and different sources of scatters arising from observation,
presence of baryons, DM mass-concentration, etc. Bayesian analysis of these
mock RCs enables us to reconstruct and identify the parameter space in galaxy
observable and theory where one can venture beyond best-fits to a preferred DM
halo model or model selections between different density models. We find that
it is imperative to choose low stellar surface density ($\Sigma_{\star}$)
galaxies for reliable cusp-vs-core distinction; for example, RC data for
galaxies with $\Sigma_{\star} \leq 2.5$ is needed for a 75\% confidence in
distinguishing cusps from cores. Similarly, we also find that for correct
estimations of the halo masses and concentrations, the RCs need to be measured
to at least a radial distance $\geq 0.8r_s$ where $r_s$ is the scale radii of
the corresponding DM halo density profiles. Out of the total $\sim$ 135 SPARC
galaxies, using our reliability criteria, we find that only 21 RCs clear the
bar to be used for any unbiased cusp-core distinction as well as DM halo
mass-concentration estimates at $\geq$75\% reliability confidence level. With
$\geq$66\% ( $\geq$50\%) reliability settings, the sample size increases to 44
(59). Interestingly, in the $\geq 75$\% reliable subsample, there are 5 times
more galaxies that are reliably cored than cuspy. [Abridged]
