In theory you control who is added to an iMessage too, but Apple’s closed source software is what does the controlling. Enter a government wiretap, and boom.
I was addressing the "closed source software" aspect, because some level is trust is required in the server for key distribution regardless of source availability.
Yes. In the iCloud Keychain model, the key client (written by Apple, “operated” without review by you) is free to add additional keys to your account that you will use to encrypt messages to you.