It seems that Node Hierarchy uses the "edit own/any content-type content" permissions to determine whether or not to display the Children tab.

However, when using Workflow, these permissions are deliberately disabled - even for users that can edit these nodes.

Also (whether or not Workflow is being used) those who cannot edit a node may still have a need to see its children. So I think that the display of the Children tab should ideally be determined by a dedicated permission.