You're right for non-citizens.

For citizens, no one needs to believe it. You give them your empty phone and they can't download your phone contents and contacts.

Generally, within 100 miles of a border (which includes international airports) there is not a warrant required for a search.

Which is where 99% of people live btw

They can search as much as they’re able to, but they can’t compel a citizen to supply a passcode.