Session Activity shows start time when session was generated not when customer connected

I understand why this is from a technical point of view, but for billing purposes the actual session start time is necessary. I had a client today that I opened a session for and emailed it to her, before she connected, she then had to reboot and was hit with Windowsupdate is installing 1 of 41 updates. She said she would call me back when it was done.
When she called back I failed to note the time and completed the work, when I consulted Session Activity Reports on G2A to my dismay I found the session start time was that initial opening of the session, not when the user connected.