I'm one among many (a majority?) of people who don't find anything about the NASA director sweating an oath particularly "solemn." You might find that your "shared solemnity" isn't so shared if you asked around.
Besides: solemnity isn't particularly bound to an object; the ritual seems more important. It wouldn't detract from your experience to not realize that I had preserved the bible's cover but replaced the pages with a hot-rodding magazine.
An object has the potential to undermine the solemnity of a ritual. As to your hot-rodding example, there is no supernatural power I'm referring to, merely perception.
Besides: solemnity isn't particularly bound to an object; the ritual seems more important. It wouldn't detract from your experience to not realize that I had preserved the bible's cover but replaced the pages with a hot-rodding magazine.