When I first started using Feedly it was just a shiny veneer over Google Reader and it kind of still is. Notice that without the extension there's no login on their site. They've assumed your feed information from Google Reader into their extension, but they haven't yet produced a version that they can host. They probably didn't have hardware that could handle their user base offline before Google announced Reader is shutting down. The way the extension currently works, you could probably host feedly.com from a laptop.