What kind of example are you talking about? Historians words and those of a textbook writer on the historiography of a historian don't usually overlap. Unless you're talking about a history textbook on the same topic/based on the work of the historian. In the latter case the historian would be preferable. However, the what is history section is not focused on historical events as such as it is about the historians and the concept of history.
If you're talking about a historian you should use the historians words and those of people evaluating him. Historians don't always have a clear cut quote of the aim of their history whereas a reputable historians might have a sentence that concisely describes what you want and it will hold more authority than your own words.
You can't really say what is right to use overall...it is up to you to make a judgment on the specific situation at hand.
I've used both i.e. historian quotes and authors views on the historian. Either way it is a quotation from a source. History Extension of course is about how historians see history, you can go the next level and see how other historians see other historians.