Fundamentally, there are crimes that transcend the boundary of the origin of the place where crimes were/are committed. As such, there are a plethora of Universal Jurisdictions that most of the countries have ratified and duly accepted its legality and scope of prosecution of an individual and an organization who have committed crime that falls under those statures. These statures mostly came as a response to moral obligation of the world to fellow human beings. Principally, they act as an assurance to enforce laws at elements egregiously violating the universal human rights (there are many inequitable cases that don’t verily translate to aggression, but we can be fairly certain when there is genocide, tortures, and persecution of dissidents etc). The perpetrators have an utter disregard to their own constitution and a universal right is least of their worries, especially in third world countries where human rights violation is rampant and casual! These statures are a weak form of deterrence, but deterrence nevertheless. Nonetheless, they make sure (at least in paper) where an intervention is needed and specify objective cases for trying a person/organization for alleged human rights violation, and strip them of the immunity they might otherwise enjoy in their home country.

I see that your primary issue is about the sovereignty of a nation, and conversely the right of a nation to prosecute an individual of crimes committed outside of that nation. Mostly, the nations that detain and try individuals who were/are in a position of higher authority and had direct accountability of the crimes committed under their guardianship. There is no arbitrary reason to detain an individual, and if he/she is wrongly detained, there is a due process that is to be followed and as a result, a possible restitution is paid to the person wrongly tried. As had been mentioned earlier, even the powerful nations mostly fry the big fishes of small nations- but that’s a about enforceability and willingness to trade for the bilateral relationship with the counterpart nation.

And yes, Bush had been accused of crimes against humanity for certainly committing crimes in U.S. among others; Guantanamo Bay: although it is a territory of Cuba, U.S. leased from them and is technically a U.S. territory.