You need to make a clear distinction on what "history" is defined as.
History is the events that occurred in the past, but to what extent has our understanding of history been influenced by the interpretations and perspectives of historians?
It's not safe to assume historians don't own history, because you haven't defined history yet. Do past events have meaning without the influence of historians? Why is it that there are numerous schools, numerous fields, different interpretations? Yes the past events are an objective occurrence, but how do we know what has happened without historians telling us the 'story'? If we take a simple, yet sophisticated history - the history wars of Australia, is oral testimony acceptable as evidence of what happened? Are the only reliable records the records which the white settlers owned?
If we don't know what has happened, what history do we have? Yes, on an objective scale, something did happen. We need to be told what has happened in order for us to understand the history. But as humans, in a (post)post-modern era, with many old-school schools still influencing society (such as empiricism, revisionism etc.), we may misconstrue the truth, however, this becomes our personal truth, this becomes what we understand as history.
You might think history is black and white, and there are many events which are black and white. But historians write the history, they write according to the existing social policies and practices of the country and time. Why do we not accept say a Marxist view of history? Why isn't the Aeneid a reliable source? At their times, the historian writing about that event believed that their history is history. We can look at in from a contemporary point of view and say it's inaccurate, but maybe 200 years later, our descendants will say our interpretation is wrong even though right now, the way I record an event is what I believe to be as objective as possible and the history is as objective as possible.
So the historian does own history in many respects, they need not determine what can go in and what can be left, but they are influenced by society and it becomes their history. We have evidence of a past event, but the history of that event needs to be written, and it is in that action of writing which the historian owns.
I should point out that this is my understanding, whether it's right or wrong is based on how strong I can make an argument. When you write your essay, you could be arguing something which the marker disagrees with, but as long as you have the evidence/sources/historians to support your view, your response will be fine.