@Hollow7F her average time was originally as stated, 1:15 minutes on April. Doumeki changed that. Why he chose her specifically, was PROBABLY because in terms of contracts completed, she wasn't very high, while Shin was. So he figured if he swapped the two nobody would notice. There's a lot of holes sure, but it nonetheless does prove that he did change it.
He only changed three peoples' times. Shin, Ume, and Yariba
Yariba proved he was framed, but technically didn't prove Doumeki was the culprit. The first part was just more important, since the company was looking for a scapegoat. Whether or not the second part is true (which is probably is) is just a side bonus to the company