What is the truth about Barbara Graham the 1957 film portrayed her as an innocent victim?

I have seen that movie and Hayward won an Oscar for her role as Barbara Graham, but although the movie was inspired by the true story, the similarity stops there. Graham was convicted of killing an elderly woman in an attempted house robbery. Without provocation, Graham beat the poor woman senseless, until she finally bashed the woman's head so badly there was no possiblity for life.

As it turned out, the woman had no money or expensive jewelry, they just had their information mixed up. On June 3, 1955, Graham and her partners in crime were executed in the gas chamber at San Quentin Prison in San Francisco, CA.