You're describing S3, not their customer Dropbox. Adding a sharing layer on top is something easily replicable.
Considering that Dropbox is the one company that has just "made it work", I wouldn't be so sure of that. Syncing isn't always easy and at scale the problems are that much bigger. Mix in cross platform issues (not just Mac/Windows, but mobile too) and it gets that much more interesting.
You're absolutely right that syncing is a classically hard problem that Dropbox has addressed impressively well for consumers.