  The $\sim 5\sigma$ mismatch between the value of the Hubble parameter
measured by SH0ES and the one inferred from the inverse distance ladder (IDL)
constitutes the biggest tension afflicting the standard model of cosmology,
which could be pointing to the need of physics beyond $\Lambda$CDM. In this
paper we study the background history required to solve the $H_0$ tension if we
consider standard prerecombination physics, paying special attention to the
role played by the data on baryon acoustic oscillations (BAO) employed to build
the IDL. We show that the anisotropic BAO data favor an ultra-late-time
(phantom-like) enhancement of $H(z)$ at $z\lesssim 0.2$, accompanied by a
transition in the absolute magnitude of supernovae of Type Ia $M(z)$ in the
same redshift range. This agrees with previous findings in the literature. The
effective dark energy (DE) density must be smaller than in the standard model
at higher redshifts. Instead, when angular BAO data (claimed to be less subject
to model dependencies) is employed in the analysis, we find that the increase
of $H(z)$ starts at much higher redshifts, typically in the range $z\sim
0.5-0.8$. In this case, $M(z)$ could experience also a transition (although
much smoother) and the effective DE density becomes negative at $z\gtrsim 2$.
Both scenarios require a violation of the weak energy condition (WEC), but
leave an imprint on completely different redshift ranges and might also have a
different impact on the perturbed observables. They allow for the effective
crossing of the phantom divide. Finally, we employ two alternative methods to
show that current data from cosmic chronometers do not exclude the violation of
the WEC, but do not add any strong evidence in its favor neither. Our work puts
the accent on the utmost importance of the choice of the BAO data set in the
study of the possible solutions to the $H_0$ tension.
