To me, it reads like this: Google is going to prevent users from storing users' data elsewhere. As if it's Google's data, not users'. Though with the free tier this as well may in fact be the case :-/
I also imagine there is the other side where the third party has crap data security. End users figure that their data is safe with Google and may not consider that there is a third party with their various levels of security.
I can see Google copping a lot of heat should Company X have a data leak and that data was originally gathered from a users Google data store, whether it is justified or not.
It's going to be "Gmail data breached".