The lack of communication kind of makes it sound like there's a 2-sided problem. The Server Administration should should in fact have the ability to back up just about anything they please, but that doesn't mean that how, when and what method is their purview and no one else's. Of course - I'd say that's not solely up to them on ANY amount of data: there has to be consultation and agreement as to what data is retained in what way and for how long, and that's a discussion needed to happen between the business unit owning the data, and the unit performing the operation.

In almost every case - third party apps going in and pulling backups via their own customized agent have caused me issues of one kind or another. Also - the one-size-fits-all approach to backing up everything in the same way on a SQL server, well, just doesn't make sense. Some data is deemed critical, and should be treated differently.

That being said - once the rules are established, and the responsibilities for safeguarding the data properly line up with those units doing each step of the work - there really isn't a conceptual problem with someone other than the DBA "running" the backups. It does however require ongoing discussions between the two groups from now on.