This is a good question: generally if all you know about someone is their twitter name, and that's it, then a compromise of their twitter account could lead to a compromise of their key announcement.

Even this case is mitigated because of the timestamping: a compromise would have to be a public compromise on an ongoing basis, and everyone in the world would have to see the same compromise, including the alleged twitter holder. Tracker statements add to the timestamping: when someone runs the Keybase client and tracks them, they sign a statement saying on date X twitter user Y had that public key and they checked it.

The second advantage is that a person is typically a sum of many identities. Consider a known developer who signs code using their Keybase announced key. (Let's say Jeremy Ashkenas does (does he?) - anyway, he's on Keybase as https://keybase.io/jashkenas). His public key is announced on his Github and Twitter accounts, both of which are known. He signs those statements with the matching private key. If you ask Keybase for his key, you get 3 things: Keybase telling you what it is, Twitter agreeing with you, Github agreeing with you, and bitcoin telling you everyone in the world has gotten the same answer for those 3 accounts for the last few months. And CLI tracker statements timestamping, too.