I don’t think you’re following the argument, which is that swearing an oath over something like Sagans book doesn’t mean as much because the person making the oath doesn’t believe Sagan will hold them accountable.

I follow the argument just fine, but it's fallacious. You should keep your word because it is the right thing to do, not because some invisible boogeyman will toss you into hellfire if you don't. If someone can't be motivated to serve the public good without the background threat of eternal damnation, perhaps they are not mature enough yet to be appointed director of NASA.

But the person swearing the oath doesn't believe in gods, so swearing on any of them will mean much less to them.

If the only reason to do it is because the people around them will hold their oath in higher regard - shouldn't they swear on a stack of all religious texts, and on all gods?