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$\ast$ and Sagittarius A$\ast$ (Sgr A$\ast$), using the size $rsh$ and deviation from circularity $\Delta C$ of the BH shadow. For the case of the EHT image of Sgr A$\ast$, limits on $\Delta C$ are not available due to the sparse interferometric coverage of the 2017 observations, alongside the short variability timescale of Sgr A$\ast$ compared to M87$\ast$. 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$\ast$'s shadow. The latter is quoted to be $\lesssim 10\%$ as with M87$\ast$, 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$\ast$'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.