The Border Patrol’s jurisdiction isn’t confined to southwestern deserts or isolated northern checkpoints: Federal law empowers agents to board vehicles and vessels “within a reasonable distance from any external boundary of the United States,” whether inland or offshore. “Reasonable” is 100 miles as the crow flies—meaning some 200 million people live within an expansive border zone.
They may have the power to do so in the US, but step onto foreign territory and they’re just border hopping like any other criminal. Their US powers mean nothing unless that foreign nation also provides them with diplomatic immunity or some similar power.
I think this is more a warning to immigrants and people who have family that are undocumented that if Trump gets elected, that you’re not safe 100 miles in. That’s my take, but I could be wrong.