The proxy user doesn't have access to the SQL server at all (and doesn't require it on my test machine). I gave the proxy user Windows Administrator rights, which...

Unfortuntatly, their IT department has gone into hiding and are refusing to acknowledge that they have made any other changes

I checked the batch...

When I run that, I get the expected response. The proxy user is a member of the Power Users group, and can run the commands in a CMD window...