A few other points in favour of backing up to disk ...

Everywhere I've worked as a DBA, doing backups this way neatly mirrors the departmental structure in that the DBA manages the backups to disk and the Windows Server guys manage the backups to off-line media. i.e. they don't fiddle with my databases and I don't go near their tape drives !

For most network backup solutions, you will need to buy an additional item of licenced software in order to back up your SQL Server databases directly. Backing up first to disk means this is not necessary. If you have a lot of servers this can be a big saving.

It can be difficult managing your SQL Agent schedule when you have backups taking place outside of that schedule at a time which may vary from day to day. The network backup software optimises the schedule to keep the tape drives loaded appropriately and knows nothing about your servers batch workload. If you back up to disk first this dependancy is broken.

The only good reason (IMHO) to back up your databases directly with a network backup solution is if you have very large databases and the cost of disk space is an issue. I'm forced down this route with a few servers but make sure if you go this way that you carry out regular test restores (you should anyway but in this case it becomes even more important because there are more potential points of failure).