  We observe that the errors on the Hubble constant $H_0$, a universal
parameter in any FLRW cosmology, can be larger in specific cosmological models
than Gaussian Processes (GP) data reconstruction. We comment on the prior mean
function and trace the smaller GP errors to stronger correlations, which we
show precludes all well studied dynamical dark energy models. Our analysis
suggests that "cosmological model independence", especially in the statement of
Hubble tension, has become a misnomer.
