From a legal standpoint, the reason that Lillian Pierce's testimony could not be used against Sweeney, was because Pierce never pressed charges against him. Sweeney was never arrested, or convicted, of assaulting Pierce. So in the eyes of the law, he never assaulted her. The courts can't just take someone's word for it, even if that person has medical records, the courts can only use what has been proven in a court of law.
If she had pressed charges, or even called the police and filled out a report, then perhaps her testimony could have been used. She never did any of those things, she allowed Sweeney to go free, and he wound up killing another woman.