Border security are not idiots. They know about travel mode.

Travel mode works because it can’t be changed on device and so moves the vault out of border security jurisdiction.

They can have probable cause to search your phone and will if they want to but they are unable to put you in a room with a browser and make you download something, so hence it’s out reach.

It could be he works for US government and protects himself from say EU border guards. Who are far less intrusive. But better save than sorry.