I don't see how that changes anything except to make the analogy politically fraught and easier to derail. The logic remains the same. Certainly, conservatives have no problem with the logic if you modify the analogy as you have suggested.
If this is actually your point then you are supporting root's argument, not rebutting it. Root was pointing out poor causal relationships determined from lack of recognition of confounding variables. You just listed another (substantially more famous) example of such a relationship.