I have the same issue and I don't think Vmware should have closed your case with that answer. If SQL Express isn't supported that is fine, but if SQL 2008 R2 is also installed on the same server, that is supported and should be able to be backed up. At the moment I can't install the VDP SQL agent the same as you as some app has installed SQL Express 2012, so I can't backup any of my SQL 2008 R2 databases. VMware needs to provide a way for the agent to work with SQL 2008 R2 when they both co-exist. I don't care if my SQL 2012 Express DB doesn't get backed up, but I NEED the SQL 2008 R2 databases to be backed up.
I am hoping they have fixed this in 6.1 but haven't been able to try it yet.