What security regulations apply to US private airstrips?
Private airports have very little security and light aircraft flying within a country typically aren't required to file a flightplan and aren't required to have transponders for secondary radar. You can get in a private aircraft and fly off pretty much as easily as you can get in a car and drive off.

Private aircraft crossing international borders are subject to much stricter requirements. In the case of flights from mexico to the USA they will be required to have a transponder, to file details of the flight with the authorities in advance, to land at the first available airport of entry and to maintain a certain altitude so they remain visible on radar. At the airport of entry CBP (customs and border protection) will gather will check passports/visas, gather customs declarations and may inspect the plane. If you want to know the gory details take a look at http://www.cadds.com/bcpilots/docs/CrossBorderManual.pdf .

There is a section of airspace surrounding the USA and Canada called the North American ADIZ. All aircraft in that zone are required to identify themselves. If an aircraft is spotted in the ADIZ cannot be identified then it may be intercepted by fighter jets.

But a small plane flying low with the transponder turned off is pretty hard to keep track of on radar and if the criminal can slip undetected through the ADIZ he can easily find a quiet private airstrip to land at.