US border patrol gives no shits about most laws and international treaties. Supposedly they are conducting a reasonable search there, so if they unwittingly encounter classified information in the course of that duty, they most they might need to do is report it.

Anecdotally, I have heard cases of some workers bringing a fresh laptop through the border, then re-imaging it with their files after. This is probably what government with classified files, corporate agents holding trade secrets and diplomats with sensitive info need to do.