Normally, the behavior with UIDocumentPicker is that you present, then the user must use the \"Locations\" menu on the top right to switch between the services. Is it possible t
This isn't specifically about Google Drive but at a past job I needed to display Facebook when Apple SDK wasn't showing me Facebook. (The edge case here was the user's Facebook account wasn't in Settings.)
So I grabbed their icon and made a custom entry.
I suspect that you could do the same here. Grab the Google Drive icon and make that a custom Document. And when the user selects it, you hand them off to Google.
This is just a guess since I've not used UIDocumentPicker. And also, it is quite hackish.