Absolute rights. These rights cannot be limited in any way. They can not be reduced or amended. Examples include the right to protection from slavery or torture. Limited Rights. These rights come with exceptions. An example is the right to liberty, which can be lawfully restricted. Lawful arrest is an example of a limited right. Qualified Rights. Government interference with these rights is allowed in special circumstances, and only when necessary in a democratic society. The interference must fulfill a pressing social need; pursue a legitimate aim; and be proportionate to the aims being pursued. An example is government restrictions on the right to assembly and association, in order to calm a riot. So an unqualified right is one where there are no qualifications - unrestricted. The United States wants unqualified right to inspect ANY facilities it wants, not as defined and limited by the government of Iran. For example, Iran is not allowing inspectors to inspect certain facilities as part of the old deal.

its badly written because it has the word don't in the sentence. so it is actually saying they "do not" have the rights whether you interpret unqualified to mean unqualified as in unqualified to do a task because of no training. Or unqualified in the sense of having the right. Either way, the sentence is suggestive of a possible "double negative".

In this context it means they can inspect the locations and military facilities whenever they want. They don't have to ask permission to do so.