Access control in Beaker is through that private key - you need it in order to edit the 'dat' (name for a synced folder). So, no, there aren't a lot of complex permissions available - but you can also separate an app into several dats and use a master one to manage the permissions of those. Not terribly complex, but it's actually surprising how much you can do. (It's tough to wrap your head around not having a server - but it's actually true.)
But help me out - I think alot of the Web falls into this category:
* User logs in to edit their data (has private key to their dat). * User shares their data (blog, photo feed, whatever) with others (who don't have the key). * Those others merge all incoming feeds into a single master feed.
You could replicate YouTube, Facebook, Twitter this way - usually there are not complex permissions in these apps, are there? (Not that you'd want to replicate them...)