It's actually worse than this; this map neglects the zones around international airports.
IIRC they asked for those but they didn't get them because the other federal law enforcement gangs didn't want their turf encroached on. Did that change?
I don't believe many of the things the border patrol does is actually intended in law. They like to claim it is, even bring out all sorts of papers, but in reality its stretching the whole idea so far it wraps around space-time. Border inspections were written in the constitution to support finding people who are avoiding duties and tariffs.