I received a google drive update tonight and I'm now able to save my database. I have the file set as available offline and I access it from a Drive shortcut directly to the file.
The version on my Samsung Galaxy S5 is 2.3.631.16.35
The version on my Nexus 5x is 2.3.631.16.40
It's interesting that you just posted this a few days ago because I think the permission problem has been there for non google drive file types for about a year now, but it's working now.