I believe an accounts basically stores your public key on their servers, so other people can verify with FireChat who it is that sent the message.

In an offline context, you'd be able to get a lot of messages and tell that it's the same person talking, but you'll have no way to see whether that really is the person or not. FireChat's public key servers allow those with access to see- according to FireChat- who is talking.

How are you supposed to verify with FireChat who sent the message when you don't have an internet connection though? Are you supposed to route your (presumably encrypted) request through other (presumably connected) phones? What's the point of requiring an account when the their entire selling point is that you can use the app in places with no internet access at all, like the wilderness?

This is easy to implement using cryptography. E.g. when firechat assigns a username, they sign your certificate for said username using their key.

Then, when sending messages, they have to be signed with your key (or outright encrypted), and the receiver verifies the key is correctly signed using firechat's key.

You can impersonate other users.