  The most recent Hubble constant ($H_0)$ estimates from local methods (z <<
1), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshifts
$H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$
confidence level. Within this context, Lima & Cunha (LC) derived a new
determination of $H_0$ using four cosmic probes at intermediate redshifts
($0.1<z<1.8$) based on the so-called flat $\Lambda$CDM model. They obtained
$H_0=74.1\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$, in full agreement with local
measurements. In this Letter, we explore the robustness of the LC result
searching for systematic errors and its dependence from the cosmological model
used. We find that the $H_0$ value from this joint analysis is very weakly
dependent on the underlying cosmological model, but the morphology adopted to
infer the distance to galaxy clusters changes the result sizeably, being the
main source of systematic errors. Therefore, a better understanding of the
cluster morphology is paramount to transform this method into a powerful
cross-check for $H_0$.
