An anticorrelation between the central density of the dark matter (DM) halo (ρ150, DM) and the pericentric distances (rp) of the Milky Way's (MW's) dwarf spheroidal galaxies (dSphs) has been reported in the literature. The existence and origin of such anticorrelation are, however, controversial, one possibility being that only the densest dSphs can survive the tidal field towards the centre of our Galaxy. In this work, we place particular emphasis on quantifying the statistical significance of such anticorrelation, by using available literature data in order to explore its robustness under different assumptions on the MW gravitational potential, and for various derivations of ρ150 and rp. We consider models in which the MW is isolated and has low ($8.8\times 10^{11}\, {\rm M}_{\odot }$ ) and high ($1.6\times 10^{12}\, {\rm M}_{\odot }$ ) halo masses, respectively, as well as configurations in which the MW's potential is perturbed by a Large Magellanic Cloud (LMC) infall. We find that, while data generally support models in which the dSphs' central DM density decreases as a function of their pericentric radius, this anticorrelation is statistically significant at 3σ level only in ${\sim} 12~{{ \rm per\ cent}}$ of the combinations of ρ150 and rp explored. Moreover, including the impact of the LMC's infall on to the MW weakens or even washes away this anticorrelation, with respect to models in which the MW is isolated. Our results suggest that the strength and existence of such anticorrelation are still debatable: exploring it with high-resolution simulations including baryonic physics and different DM flavours will help us to understand its emergence.