I had actually thought about something along those lines, although I was thinking of doing a stored procedure that they could call.
Maybe set it up to allow them to choose the directory and the DB to backup to.
At the moment, I'm still sort of feeling my way into the job, finding out just how much I can or cannot do with the servers (the systems are very firmly locked down, although not so far that I haven't been able to do my job yet.)
There's a fairly solid separation of duties, too.
There's a person responsible for configuring the backup application used (CommVault) who is quite easy to work with as far as setting up schedules for the backups (and knows enough about SQL to understand WHY the TLog needs to be backed up)
There's a couple people responsible for adding / removing / changing users (including service accounts) in the domain (again, fairly easy to work with)
There's my "partner-in-crime" who's responsible for the Oracle systems, and who I am supposed to be cross-training / being cross-trained by.
Then there's the developer who was covering when the previous DBA left.