Earlier quoted context omitted.
As kawera said two comments above yours: Their servers do not store unencrypted messages so they need to come from the phone. ---- That's why some people criticise Telegram: Their messages have to be stored unencrypted for their setup to work.
AFAIK Apple Message implements encryption and has independent clients. So I think the problem can be solved with some effort.
This scheme has various weaknesses, eg. a rogue key could be associated with someone's account without their knowledge, and anyone who sends this person messages will therefore be sending a copy encrypted with the rogue key.