Once again, the only reason that someone is ineligible to be vice president is if they are ineligible to be president, so the distinction is moot. The author posits very different reasons why Bill and Hillary are ineligible to be president, and that hardly meets the condition of "precisely".
If you want to continute to engage in absolutely futile nit-picking defense of one phrase in a thoroughly discredited article, go ahead and I cede the field to you now.
True, but it still is a reason - and that makes it the same reason for both of them.