It's only half of the solution though. If the models are trained in a closed way, they can prioritize values encoded during training even if that's not what you want (example: ask the open Chinese models about Tiananmen). It's not beyond imagining that these models would e.g. try to send your data to authorities or advertisers when their training says so, even if you run them locally.
So the full solution would be models trained in an open verifiable way and running locally.
The model is only generating tokens without touching the network at all, right? How would it send data away?