Even though you can't  modify the tasks you can see the link handles which are usually used for linking different tasks. They shouldn't be displayed when the RadGanttView is in read-only mode.

Workaround: handle the GraphicalViewItemFormatting event and manually hide the link handles: 

        private void radGanttView1_GraphicalViewItemFormatting(object sender, GanttViewGraphicalViewItemFormattingEventArgs e)
        {
            GanttGraphicalViewBaseItemElement itemElement = e.ItemElement as GanttGraphicalViewBaseItemElement;
            if (itemElement != null)
            {
                Console.WriteLine(itemElement.LeftLinkHandleElement.Visibility);
                itemElement.LeftLinkHandleElement.Visibility = Telerik.WinControls.ElementVisibility.Collapsed;
                itemElement.LeftLinkHandleElement.PropertyChanged -= LeftLinkHandleElement_PropertyChanged;
                itemElement.LeftLinkHandleElement.PropertyChanged += LeftLinkHandleElement_PropertyChanged;
                itemElement.RightLinkHandleElement.Visibility = Telerik.WinControls.ElementVisibility.Collapsed;
                itemElement.RightLinkHandleElement.PropertyChanged -= LeftLinkHandleElement_PropertyChanged;
                itemElement.RightLinkHandleElement.PropertyChanged += LeftLinkHandleElement_PropertyChanged;
            }
        }

        private void LeftLinkHandleElement_PropertyChanged(object sender, PropertyChangedEventArgs e)
        {
            GanttViewTaskLinkHandleElement linkHanle = sender as GanttViewTaskLinkHandleElement;
            if (e.PropertyName == "Visibility" && linkHanle.Visibility == Telerik.WinControls.ElementVisibility.Visible)
            {
                linkHanle.Visibility = Telerik.WinControls.ElementVisibility.Collapsed;
            }
        }