Oh I know, but it really gets complex with those types of political issues and with the video documentary that came out of there, I think it was Shane Smith at Vice Media, it really looked like this thing in Mexico has been a Jesuit run operation.
The Jesuits know how to play hard core, but this is not the 1600s either. The Bishop running the thing is a wee bit of a rogue too. If a drunken lout like Shane Smith could get to him, the Mex government could too.
The way you deal with those sorts of diplomatic situations will vary a lot, and in those countries people know how to play. I went through a class on it in the 1980s that was taught by some SF and CIA people who had experience in Afghanistan. A lot of times the official guy in charge is just a figurehead. One of the SF guys figured out after a few days that the "bodyguard" who met them right after they were dropped in and stuck with them the entire time was the actual tribal military commander. When they were introduced to the "subchiefs" and "leader", the "bodyguard" would position himself behind the SF guy who was doing the talking, and then would use subtle hand signals and facial expressions to indicate what he wanted the fake "chief" to say.
As for us dealing with our government. I think that depends. I take my clue from how the various diplomatic agencies do it. They have declared agents and officials, and then the "illegal operatives". What you can't necessarily do though is get by for very long with one group working for one set of policies and another group working for an opposing set of policies.
I would also point out that while criminal groups in Mexico are usually called "drug cartels", it is often not so much the "drug business" that ticks everyone off, it is the constant robbery, murder, and thugging which goes along with the quality of people who end up controlling those businesses.