How would they know? How would they prove it?

There's a known case a few years ago where a woman was trapped away from the US for 3 years - her estranged husband put her on the list when she went to visit her parents, and boom, she's not allowed into the US and no-one will tell her why, making it easy for him to get divorced and keep the house.

(If she'd known what had happened, and been able to put her hands on enough money, she could maybe have flown to Canada/Mexico and entered overland; all she knew was she was denied boarding)