I think that the terminology used in Qt with model/view controls is flawed. On their explanation page they state, that they simplified the MVC to MV by merging View and Cont
I think that ... What they call Model is in fact Controller only.
No, their "model' is definitely not a controller.
The controller is the part of user visible controls that modify the model (and therefore indirectly modify the view). For example, a "delete" button is part of the controller.
I think there is often confusion because many see something like "the controller modifies the model" and think this means the mutating functions on their model, like a "deleteRow()" method. But in classic MVC, the controller is specifically the user interface part. Methods that mutate the model are simply part of the model.
Since MVC was invented, its distinction between controller and view has become increasingly tense. Think about a text box: it both shows you some text and lets you edit it, so is it view or controller? The answer has to be that it is part of both. Back when you were working on a teletype in the 1960s the distinction was clearer – think of the ed – but that doesn't mean things were better for the user back then!
It is true that their QAbstractItemModel is rather higher level than a model would normally be. For example, items in it can have a background colour (a brush technically), which is a decidedly view-ish attribute! So there's an argument that QAbstractItemModel is more like a view and your data is the model. The truth is it's somewhere in between the classic meanings of view and model. But I can't see how it's a controller; if anything that's the QT widget that uses it.