I think I would feel reasonably comfortable telling a border agent that I didn't bring a phone / specific data because I felt uncomfortable about the idea of ha

I think I would feel reasonably comfortable telling a border agent that I didn't bring a phone / specific data because I felt uncomfortable about the idea of having it searched at the border. There's certainly nothing wrong with that, and I doubt it would get you denied entry (unless they pulled you out for a non-routine reason anyway). You're certainly not required to bring anything across a border.