True, U.S. law does not apply in Mexico - but Mexican law does not apply in Mexico either. Mordida, not Mexican law controls in Mexico, that is why the Drug Cartels control Mexican cities like Nuevo Laredo. In addition, the U.S. government has hired bounty hunters to operate in Mexico to arrest drug dealers and murderers since Mexico is corrupt from the top down. Google Wikipedia and "Kiki Camarena" to read how the U.S. Government hired bounty hunters to arrest drug gang killers in Mexico. The U.S. should not cooperate with a corrupt country like Mexico in arresting Dog, a U.S. citizen enforcing a U.S. warrant.
It's true that the DEA hired "bounty hunters" but not American "bounty hunters". In 1990, they hired Mexican nationals to snatch Dr. Humberto Alvarez-Machain and Javier Vasquez Velasco and bring them back to the U.S. (See Old Puzzles, Puzzling Answers: The Alien Tort Statute and Federal Common Law in Sosa v. Alvarez-Machainm" by Mark K. Moller) This is an important and significant difference.