Apologies for the delayed response; I was out on an unexpected family matter.
This issue has evolved since I last posted. It was discovered that IT, in an emergency move of the production database to a new server, had not migrated all permissions and roles (including public) consistently. We also learned that IT's dev, test, and prod environments are not the same--either with regard to user permissions or content.
After sifting through and untangling these red herrings, the remaining problem is this:
The user I referenced in my original post cannot connect to the production database by any method except 10.0 Query Layer. This includes 10.0 SDE Service connection, 10.0 Direct Connect, 10.2 SDE Connection File, 10.2 Direct Connect, and 10.2 Query Layer. I know my original post indicated a 10.2 Connection File was successful; this inconsistency is a difficult trait of having a split shop--GIS on one side, IT on the other. They must have changed something, but I don't know what.
But here's the twist: the SDE user can connect to the production database via any method. Again, this was not true last I posted; something IT changed during this process made it so.
So, again, I am left to strongly suspect permissions as the root issue. I will post when the resolution appears.
Thanks again for your help.