The terms in question:
"You may export or extract non-programmatic, GUI-driven Twitter Content as a PDF or spreadsheet by using "save as" or similar functionality. Exporting Twitter Content to a datastore as a service or other cloud based service, however, is not permitted."
So do I own my tweets or not? If I own them, can't I decide what to do with them, such as storing them in a cloud service? Twitter can't have it both ways.