What would the advantages be of using a document management system over a relational database management system

That doesn't sound like an either/or question to me. Document Management Systems typically use an RDBMS under the hood. They also typically integrate with an indexing/search tool as well. Perhaps you're asking about the merits of an off-the-shelf DMS package versus a roll-your-own custom built solution?

And no DMS can protect against a user sending out the wrong version of a document. You can make a system foolproof but you can't make it damn-fool proof :-)