Commentary for Kiddushin 129:9

This section provides the opposite scenario to that which we saw above. The man claims that he betrothed the woman’s daughter, and is therefore forbidden to the daughter’s relatives. However, the daughter is still permitted to his relatives, since neither she nor her mother claimed that she was betrothed to him.
The mother’s relatives are permitted to him, because he doesn’t claim to have betrothed her. However, she is forbidden to his relatives because she claims to have been betrothed to him.