Baryon acoustic oscillation (BAO) measurements play a key role in ruling out postrecombination solutions to the Hubble tension. However, because the data compression leading to these measurements assumes a fiducial $\mathrm{\Lambda }\mathrm{CDM}$ cosmology, their reliability in testing late-time modifications to $\mathrm{\Lambda }\mathrm{CDM}$ has at times been called into question. We play devil’s advocate and posit that fiducial cosmology assumptions do indeed affect BAO measurements in such a way that low-redshift acoustic angular scales (proportional to the Hubble constant $H_0$) are biased low and test whether such a rescaling can rescue postrecombination solutions. The answer is no. First, strong constraints on the shape of the $z\lesssim 2$ expansion history from unanchored Type Ia Supernovae (SNeIa) prevent large deviations from $\mathrm{\Lambda }\mathrm{CDM}$. In addition, unless ${\mathrm{\Omega }}_m$ is significantly lower than 0.3, the rescaled BAO measurements would be in strong tension with geometrical information from the cosmic microwave background. We demonstrate this explicitly on several dark energy (DE) models ($w\mathrm{CDM}$, CPL DE, phenomenologically emergent DE, holographic DE, ${\mathrm{\Lambda }}_s\mathrm{CDM}$, and the negative cosmological constant model), finding that none can address the Hubble tension once unanchored SNeIa are included. We argue that the ${\mathrm{\Lambda }}_s\mathrm{CDM}$ sign-switching cosmological constant model possesses interesting features which make it the least unpromising one among those tested. Our results demonstrate that possible fiducial cosmology-induced BAO biases cannot be invoked as loopholes to the Hubble tension “no-go theorem”, and highlight the extremely important but so far underappreciated role of unanchored SNeIa in ruling out postrecombination solutions.

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• Cosmological parameters
• Dark energy
• Dark matter