Earlier quoted context omitted.
Problem is: the rights as worded by Google allow a whole lot more than the reasonable-use wording by Dropbox. Remember that recent flap about iOS apps uploading users' entire Contacts list for non-relevant uses? hey, users gave permission for the apps to access that data without explicit limits; same idea, same concerns.
No. If they are to enable you to share a document you need to give them license to do so. If they are to create copies of the files across datacenters and employ OCR on images and use that to improve their algorithms, they need to inlucde that in their terms of service to avoid getting sued.
That's very different from what you are describing.