If _I_ were running a email hosting service, _I_ would periodically hook up a tape drive, back up everything to tape, and remove the tape. In fact, I'd use different sets of tapes for different days of the week, so that if malware got in I'd have time to detect the problem before all the backups were contaminated. It's hard to erase tapes which are not even in the tape drive. It's even harder to do it multiple times because I have multiple sets of tapes. Backing up to tape means that the latest mail won't be backed up, but it would be a whole lot better to be out a few hours or even a few days of mail than to be out of _all_ mail.
For those who don't like tape, back up to a _removable_ drive... and remove it once the backup is completed. Again, have at least one removable drive per day per mail server, and physically remove the drive when the backup is done. All of my backups at work are to tape, with a nice 5TB removable drive covering the important stuff as well. Tape is slow, old-fashioned... and works. Hipsters and millennials will pry my LTO tape drives out of my cold dead hands.
It sounds as if all backups were live, online, backups, so that the backups were killed at the same time as the main systems were killed. This means that, effectively, there were no backups. They're fucked.