Yes, this, and a second part: GDPR recognizes that data moves between services, and people should have rights about their data that can be enforced on recipient

Yes, this, and a second part: GDPR recognizes that data moves between services, and people should have rights about their data that can be enforced on recipients after data is transferred. Currently, agreeing to transfer is a ratchet, where the secondhand party has basically no responsibility to you.