As the administrator of the Misaka Network, Last Order KNOWS what sort of things Accelerator did to the members of the Network before. I don't think she ever says it. But she knows.
She also knows Accelerator refuses to ever let his past deeds go unforgotten.
This is the great paradox of the series: Accelerator is a man who tries to do good and is often called evil. Touma is a man who does what he feels like and is often called good.
