As at August 2015, the 'Drive API for Android' is not functioning as (loosely)documented, is effectively broken. The main sore points are as follows:
1) An app sharing the same APP_ID and logged in with the same Google User is meant to be able to find and access the same files as Google indicate (e.g. appX on device1 creates a folder named 'blahblah' (where no 'blahblah' folder already exists in the User's Drive), appX on device2 should be able to find that folder and upload/download files from it also...however this is not the case (or if it does work, it is intermittent and mostly not working at all)). This remains the case even after (many) requestSync calls and over 72hours of allowing Drive to sync itself.
2) A trashed folder is not observed as trashed, even after a requestSync call has succeeded. Such a trashed folder will still have isTrashed==false.
3) A permanently trashed folder (i.e. it is GONE from Drive, it is never coming back). Can still be found and "successfully" have folders and files created within it, however writing to such a file's contents will always yield a failure in Completion Event Service. Again, such a folder will still have isTrashed==false (which is abysmal).
Bug reports have been lodged (thanks to @DalmTo for the link) via: https://code.google.com/a/google.com/p/apps-api-issues/issues/entry?labels=Type-Defect,API-Drive
https://code.google.com/a/google.com/p/apps-api-issues/issues/detail?id=4003 https://code.google.com/a/google.com/p/apps-api-issues/issues/detail?id=4004
SO, the question: know a way around these issues?
UPDATE:
I've narrowed these problems down to my personal Google account (or my personal Drive, which has many, many files in it). That suggests these issues are symptoms of or closely related to https://code.google.com/a/google.com/p/apps-api-issues/issues/detail?id=3905