Sophisticated method: Tape backup systems (the one we use, for example) will work with a purchased agent that can be installed on the SQL Server's server. When the tape backup system wants to back up, it contacts the agent, which contacts VSS (a SQL Server service on the SQL Server) to back up the databases to tape.

Dumbed down method (the one we use): Pick a time which is likely to be before the tape backup window of opportunity, and create a SQL Server maintenance plan/job which backs up the databases at that time to a specified folder (for example, SQLBackup). Tell the tape backup system to back up folder SQLBackup. This method wastes resources, including the space needed for the backups (stored on disk as well as on tape), I/O (writes to disks and then copied to tape), etc. We use it because our databases tend to be small, that is, 100 MB to 1 GB, and we have long windows for backup.

I have so many questions for your network admin, you really really need a better relationship with that person. (Example of questions--what are the SAN backups doing? And are they interfacing correctly with SQL Server? If so your backups may be right there ...) Perhaps you can convince the network admin that they could solve some of their existing problems if they worked more closely with you... Good luck!