Does on-device processing guarantee privacy?
It establishes a location for a processing step, not the behavior of the entire application. The app may still store results, synchronize them or request data from connected accounts. Follow what happens before and after that local step.
Local computation and local retention are different claims
Ask whether the data leaves the device at any point, including backups, analytics or optional service connections. A local model can be part of a careful design, but the model's location does not describe every record the app creates.
Suppose an app summarizes a saved note locally and later synchronizes the summary to an account. The summarization step was on-device, while the output traveled elsewhere. Both statements can be true. A useful description names that sequence so the user can decide whether it fits their expectations.