Recently, Jiayi Hu and co-workers reported that they did not resolve any thermal Hall signal in La$_2$CuO$_4$ by `high resolution' measurements, setting an upper bound of |\kappa_{xy}| <2\times 10^{-3}~Wm$^{-1}$K$^{-1}$ at 20 K. Two points have apparently escaped their attention. First, thermal Hall signals with an amplitude well below this resolution bound have been detected in disordered perovskites. Second, the longitudinal thermal conductivity of their sample is significantly lower than the La$_2$CuO$_4$ sample displaying a thermal Hall signal. We find that a moderate reduction of $\kappa_{xx}$ in SrTiO$_3$ is concomitant with a drastic attenuation of $\kappa_{xy}$. A trend emerges across several families of insulators: the amplitude of $\kappa_{xy}$ anti-correlates with disorder.