I've never heard of student visa problems caused by getting married to a non-American, which seems to be what happened in the case discussed in the OP.
My cursory reading of the USCIS website tells me her fiance would need to apply for a K1,K3 visa. Being married she is entitled to rights the typical J visa holder does not have.
This is where the immigrant/nonimmigrant visa process breaks down. USCIS makes it painfully expensive to change a nonimmigrant visa into an immigrant visa. I guess what they want to avoid is having people jump the greencard queue, and marriage moves you right to the top, by flying in on a tourist visa, find a willing US citizen to marry.
If that were the actual reason, I'd be surprised if there wasn't a standard form letter or actual reason for denial. I suppose 'Go Away, We Can't Talk About It' might get used in marginal cases or when the appropriate authority can't be bothered doing the actual research.
Or they just lost at Top100 Terrorist Names Bingo.
Solution: Enter on fiance visa or a Green Card.