You cannot pick and choose one or two variables and then claim representativeness based on a numerical match. The first step is to identify the confounding variables that are likely to influence the outcome. Only after those are specified a comparison set can be defined and matching or adjustment criteria applied. Without that process, agreement on a small number of aggregate measures does not establish that the underlying populations or mechanisms are comparable.
I'll concede this, however in large-scale demographic data, when the central tendencies of two populations align so closely, it is statistically unlikely that their underlying distributions are radically different. It puts the burden of proof on the idea that Ohio is somehow an outlier, rather than the idea that it's a standard sample. Otherwise, were we to attempt to account for every confounding variable, we would be letting the perfect be the enemy of the good.