Commentary for Kiddushin 130:6

One witness might have, at certain times, some level of believability. But not when this witness is contradicted by the woman herself.
Rather, the men do not give her a divorce in order to free her to marry someone else. She is free to marry someone else even without a divorce from either of them. They give her a divorce in order for her to collect the ketubah, which according to R. Meir, can be collected from movable property.