From my experience:

1) To use the $400 voucher at delta.com, I need both the number and the name on the voucher. I have used my kids vouchers for my travel this way.

2) Once while on the phone, I gave the agent a ticket number to use for my travel. She pulled it up and was just about to apply it but the value didn't match what I remembered. We looked a little further and realized the ticket number was not mine.

So, in your case I bet it was agent error and not some intential fraud from another delta passenger