In fact, for precisely the same reason that Bill Clinton can't serve as vice president, neither can Hillary.
Considering that, according to sworn testimony from Monica Lewinsky that Bill Clinton is a male, and according to the occasionally questionable claim that Hillary Clinton is female, their gender does not come into play according to the phrase "precisely the same reason."
Come on, you are just trying to be argumentative, right? LOL Okay, I'll explain this to you as well. "Precisely the same reason" means that, according to the author, neither Bill nor Hillary can serve as VP because they are both ineligible to serve as President. So, yes, it is for the same reason; however, it would be in opposition to different parts of the Constitution. The author claims that Hillary can't serve as VP, because as a woman she's not eligible to serve as President. Bill Clinton can't serve as VP because as a former 2-term President he's not eligible to be President.
Anything else? :-)
Have it your way, Mad Hatter, because words apparently mean to you what you want them to mean. To normal folks, precisely the same reason means just that. So you can have the last word if you wish to further mangle the English language.