It's complicated.
I worked for 2 different Tribes for a number of years. It's only as complicated as the Tribes allow. It's real simple: Sovereign Nation means Sovereign Nation. When one Sovereign Nation can tell another Sovereign Nation what to do, how to do it, when to do it, etc., then one of those Nations is not sovereign, period.
Tohono Odam have always kept lines open to their fellows south of the border, when I was in the vicinity they considered Mexican cousins as kind if a charity.
As to "subject to our laws and complicated, or "sovereign nation = sovereign nation" just note another response about BP stops well north of the border; there's no reason in the world not to build a fence along the border and a barricade along the reservation perimeter.
PS: I believe that the treaties place defense in the hands of the US and not the tribe, they should have no valid legal grounds to protest BP's defensive activities along their border.