At the university level, this is patently false. Professors have wide latitude to pick the texts for their classes except in lower division classes that might be taught by a TA.

This is more nuanced than “controlled by the administration or not”.

Universities that have accreditation (typically regional accreditation for nonprofit and private research universities) have to meet certain standards for certain curriculum design. Within those requirements there is wide latitude.

That doesn't seem more nuanced between controlled by administrators or not.. An accreditation may have a minimum number of hours for Greek Classics and could expect the topic of Classical Greek Cultural norms to be compared/contrasted with modernity or it may not be mandatory to cover. That's a bit short of an accreditation telling an administration to ensure the topic is never covered or to police every unlisted topic a professor may cover.

Nah, university approves learning objectives for a course, but how the objectives are achieved is up to the professor.