Exchange difficult to backup? Just get a copy of a dedicated backup application like BackupExec and you can backup the mailstore easily ... I use BackupExec 12 to backup Exchange 2007 (full daily backup) and the performance is quite high, no downtime at all. I don't see why you would need to take Exchange offline to back it up, unless you are backing up the raw files (ouch!), which is totally unnecessary. If you don't backup the database and flush the transaction logs then the transaction logs will start growing until you are out of free disk space!
I am sorry but if your DBA's are having trouble figuring this one out then I have doubts about their professional qualifications (no offense). This kind of information can be found in TechCenter, otherwise just search Google ...