I think there's some confusion here. I believe the quoted post is referencing the reply from BA Customer Services direct to the OP, who had raised a case with them. The "me" is the CS agent who has been given information from the investigation department. BA's procedures would require that to be closed - the e-mail is doing that.

The TA separately wrote to BA proclaiming innocence. In the circumstances of the account being under investigation, BA would not have written back to the TA in response. There is, I suspect, no e-mail to share.