This is unclear and so needs clarification. There is no property on the xblock, but instead it is up to the parent to set the correct context when it renders its children. This means that when rendering just an inline child that there is no information available to the server to know whether the child is reorderable. Fortunately the client-side code knows, so it only calls this API when it knows it needs the child rendered as reorderable.

Christina had suggested renaming the view name to make this clearer, so I'll do that and add a more detailed comment.