It seems to me that the Mexicain government is and has been demanding a say in any capitol case that involve one of their citizens in our courts. Is not that a claim of a jusidiction outside of our own? That claim has also been approved by The world Court in the Hague.
The State Dept makes reference to the applicable treaty on their webpage devoted to Americans arrested abroad.
The US State Department also gets involved with US citizens charged in other jurisdictions.
Mexico can causes problems (as do some others) because they don't like to release a prisoner to the US if said prisoner could get a death penalty. On the good side though, Bush and Fox have worked out a deal where Mexico returns (with judicial hearing but no trial) anyone requested by the US Marshal's office to the US and vice versa. (Clinton didn't even try to get criminals returned from Mexico.) There are (according the local Marshal's office) several hundred such in the Albuquerque jail awaiting trial in the US. The idea is not to allow criminals to treat the other country as King-X territory.