> if you have auto-update, or if you can inject code into the client, that privacy guarantee can be revoked at any time

Anytime you use software built by someone other than you, any guarantee can be revoked at any time - the distributor can put whatever they want into the software! When a distributor makes claims about the privacy/security of a product, at some point you either trust them and take them at their word, or you don't - in which case, it doesn't matter what they say.

Unless the product is open-source and self-hosted, that is.