It's a preferred practice that I've used since SQL 4.21a in the mid(?)-'90s. It's simple, and it requires nothing more than what comes in SQL Server and the OS. If you're running a later version and certain editions of SQL Server, you can enable backup compression and save a lot of space on the backups. This method does require disk space, but it's the cleanest and simplest backup methodology. It also gives you a local copy of the database that you can do test restores with to make sure that the backup is readable.

Since database files are locked, they can't normally be backed up as a whole. SQL Server doing a database/log backup ensures transactional consistency. There are backup programs that can go in to the database and back it up while it's up and running, but I've seen performance and locking hits with these in the past and I don't really trust them. I don't know what the current state of the art are on those and whether those issues have improved. Without doing SQL backups or using an agent, your only other reasonable backup methodology would be to take the database offline and then backup the actual database files. This is not a practical solution.

My question would be what do the higher ups think is a good way do to backups? You don't need any extra money spent on additional software to do backups this way. Just make sure your backups can be restored to another database and that you're also properly doing transaction log backups.

I have been on the losing side of this argument. A previous infrastructure manager wanted to use whatever enterprise backup tool he had to back up databases directly, and eventually the IT manager sided with him. One of the things that I didn't like about that approach was I didn't have consistent backup times, which risked running at the same time as my DBCCs, and I didn't want both things running at once. In the end I really didn't care, I was on my way out the door anyway. And then my replacement quit a few months later, so I have no idea what their status is and whether or not their backups are restorable and frankly I don't care. 😉

Redgate's SQL Backup Pro is very popular among a lot of people on this site, and if I had a really big and important data store I'd definitely consider it. But most of the databases that I work with are just fine with SQL backups/OS move to media.