You’ve misunderstood. With the client code you can be sure that your messages are properly encrypted before leaving the device. If that’s done correctly, you don’t need to trust the server, because it can’t read your messages just like some attacker couldn’t.
It kind of depends on how keys are handled. If the key passes through their servers at all (and it probably does,) then they have access to the keys and sufficient information to decrypt it. it’s possible the app does send keys independent of their server- I don’t know- but I very much doubt it. if they were capable of sending keys without a server, chances are very good they don’t actually need the server for the messages themselves. (which would then ask why they do have a server.)
But with a verified build of the client code we can know that our messages are encrypted such that, even if they held on to them until quantum computers became mainstream, they’d still be properly protected.
Assuming they don’t have the keys. This is not a valid assumption so far as I’m aware.