One of the basic responsibilities of a Database Administrator (DBA) is keeping the database available 24x7x365, including making sure the database can be restored in the event of a disaster. The traditional way a DBA has met this requirement is doing tape-based database backups. A more recent development, with the popularity of virtual servers, is the idea that SAN backups (VM Snapshots) can be the primary method of backup and recovery.
There are plenty of people that are doubtful of this solution, primarily because this changes the responsibility matrix as far as who is performing the backups and who will restore the backups to resolve issues with a production database instance. If the DBA is no longer performing the backups, then that responsibility has been shifted to someone else that may not understand the severity that a crashed database server may bring to the company.
If a database server goes down, and you lose a couple of hours of data even after the database is restored, that could cost the company millions of dollars. This is much more severe that losing a file server or even an email server. These are the servers that a system administrator might be most accustomed to restoring, but a database server can have a much large impact on the business than they can imagine.
You need to have a conversation with your boss about what a shift in responsibilities mean to the business. You should recommend additional training, deeper and more through recovery testing, periodic reviews of the backup schedule, or other steps you feel are important before you just let this core responsibility slip from your control to someone else.
If disaster strikes and the recovery process goes off the rails, you will still have to help pick up the pieces so it is in your best interest to avoid the risk of failure. You can read more about this shift in responsibility here.