I agree it is impossible. I don't like their claims that they don't have access to the decrypted keys and we can prove it by looking at the code. They could have access to the keys and looking at the code wouldn't prove they don't.

I understand but I read the statement differently. It's a description of their security model simply. Sure they could be lying like any other company, so a certain amount of trust is required.

Unless you read and compiled the code yourself and run it locally, some level of trust is always required.