Dog has no arrest powers beyond the territorial limits of the United States. (See Reese v. United States, 76 U.S. at 21). Further, Mexico is a soverign nation. U.S. law does not apply in Mexico and Chapman violated Mexican law. End of story.......
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.
And if a guy like Chapman got it done before I could...bravo for him. There are some things that all of the PC laws and attitudes, and all of the "international understandings" can't make right, no matter how you dice it. Crimes like this are one of them, but that's just my opinion, nothing more or less.