http://youtu.be/eaJKPCdimLA - actual quote being (21:16 mins): 'I'm completely dedicated to Dropbox ... I mean we're starting with files but there's all kinds of other directions we can go ... we're a long long way away from you being able to sit down in front of any computer, device, and have access to all your stuff.'
The analogy that Drew used was Athena, which apparently is this infrastructure at MIT that gives you access to your stuff no matter which workstation you're on, on campus.
It all goes in cycles, and if something happens that prompts companies and individuals to lock down their files, then Dropbox and alike will go from "universal file access" service to a trivial file sharing app. Still useful, but not as grand.