[Firebase founder here] We weren't trying to be disingenuous with the title. Keep in mind that basically any web technology, including P2P ones, do actually use servers. If you're using a domain name, for example, you're probably going to use a DNS server. If you're using Google Analytics or any other addon in a web page, you'll be using their servers. If you're on a 3G connection your data is probably being proxied by a server somewhere. Even BitTorrent has trackers. The list goes on...
Our point is that you don't need to run a server. You can treat Firebase like you treat DNS -- a service that is there for you to use but that you don't need to operate.