How do you know that story is true? Would the police say if they made a mistake? Would anyone be able to find out the truth or accuse them?
By that logic, how do you know any crime story from anywhere in the world is true and not just a cover up by cops?
The person they executed admitted to being Lao Rongzhi, admitted to participating in the crimes, but claimed she was not responsible because of abuse she suffered at the hands of Fa Ziying. While false and forced confessions are absolutely a thing, hers doesn’t really fit that pattern. She acknowledged being involved, showed remorse for the killings, but distanced herself from them and minimized her involvement in violence, focusing on the robberies. After being presented with DNA evidence, it doesn’t appear that she ever claimed not to be Lao again nor did her defense seem to ever attempt to put that forward, but both of them put forward a rigorous defense to attempt to save her.
Anything is possible, but it seems from her own actions for years up until her execution that it was in fact her and she only denied it to the local police initially, hoping to be let go.