It explains a lot, but this part is not true.
19 states allow first cousin marriages under any circumstances. (And, no, West Virginia is not one of them). 25 prohibit it, though unlikely that they can enforce those laws given the recent supreme court redefinition of marriage. The remaining six permit it under certain circumstances, five of which are fairly logical:
The problem is less an occasional first cousin marriage, which was not at all uncommon in early America, than generation after generation of the same.
Exactly. We aren’t talking about a one time thing. We are talking about the accumulation of thousands of generations.