They don't have to, they can just say the phone synchronized on its own when set back out of travel mode. They will lie, of pressure you to download the data prior their search.

Again, it's not a technical problem. Abusive people are abusive.

Law enforcers are not good people because of their title, society shape them in who their are and how they behave. Currently, in the US, they are not shaped to be helping citizen.