She does not manage people. She manages a function.
That means those who promoted her probably chose to not promote her into the management of people because they saw she was a good worker... just not skilled at managing people. Nothing wrong with that. Just be honest about why you were promoted to manage a function that has no people to manage.
How is the function performed? If people are being trained, then people perform the function.
If the 'function' does not fulfill expectations, the people did not do their job, who gets whacked?