The reason that answer choice D is incorrect is that we simply do not have any support to say that the central administrations of large institutions are usually partially responsible for "most" of the details of daily operations.
Whether or not the central administrations of large institutions are usually partially responsible for the details of daily operations, we do not know what proportion of daily operations they are responsible for. "Most" is therefore not supported.
I hope this helps and please let me know if you have any other questions.