My collegue that is working with me on the current project was packaging another application that uses Oracle.
The interesting thing about it is that he ran into the same error I did: the Oracle client tries to create (and access) an Object in the Global namespace.
But he got an entirely different error message:

To confirm it was the same issue I gave a test user the Create Global Objects privilege and after logging on again the problem went away.
So I applied the same fix that I wrote about yesterday in Redirect Global Object to Local Objects (aka fix that bad app!) to this application and it worked nicely!