Looking it up I see that that dollar was
a Spanish coin. In other words, the equivalence does not hold. We should look at the equivalence between that dollar and the U.S. dollar at the time, around the late 1700s.
But even if we were to find that the dollar was nominally equal to the U.S. dollar in its time if we were to take inflation into account it would have nothing to do with it, as back then the purchasing power was much greater.
So, yeah, fun fact but if we begin to analyze it, we see that it is more complicated than you suggest.