You don't need to trust all third-parties. Crypto magic guarantees that what you need is at least ONE server being honest. If you trust Mozilla, then you have

You don't need to trust all third-parties. Crypto magic guarantees that what you need is at least ONE server being honest. If you trust Mozilla, then you have nothing to worry about, except the proof or program may be wrong ;) Third-parties are for someone who doesn't trust Mozilla. Or that Mozilla could be compromised by an unknown adversary.