Several works over the past years have discussed the possibility of testing fundamental physics using Very Long Baseline Interferometry horizon-scale black hole (BH) images, such as the Event Horizon Telescope (EHT) images of M87∗ and Sagittarius A∗ (Sgr A∗), using the size rsh and deviation from circularity ΔC of the BH shadow. For the case of the EHT image of Sgr A∗, limits on ΔC are not available due to the sparse interferometric coverage of the 2017 observations, alongside the short variability timescale of Sgr A∗ compared to M87∗. Concerning this point, we comment on the results of a recent preprint which purports to have derived new limits on extra dimensions using the deviation from circularity of Sgr A∗'s shadow. The latter is quoted to be ≲10% as with M87∗, based on the "similarity" of the two shadows: however, this is an incorrect assumption, invalidating the subsequent results. In the immediate future, the simplest tests of fundamental physics from Sgr A∗'s image will therefore mostly have to rely on rsh, whereas additional observables such as the photon ring and azimuthal angle lapse should soon be available and allow for novel tests.