I believe that at the time, Yale was actually not co-ed, and so she was talking about girls who knew guys at Yale, but who were not actually Yale Girls.
I think to be technically accurate, you need to rephrase.
You say "Theodore Roosevelt was the only U.S. President not sworn in on a Bible.", but then you describe that Franklin Pierce was not sworn in. Therefore, Franklin Pierce was not sworn in on anything, including a bible. A more accurate, but still enticing, way to put it might be, "Theodore Roosevelt was the only U.S. President sworn in without a Bible."
You say "Theodore Roosevelt was the only U.S. President not sworn in on a Bible.", but then you describe that Franklin Pierce was not sworn in. Therefore, Franklin Pierce was not sworn in on anything, including a bible. A more accurate, but still enticing, way to put it might be, "Theodore Roosevelt was the only U.S. President sworn in without a Bible."
Thanks for the stream of neat stuff,
-Dan