It's actually simpler than you thought: In OnGUI, what's drawn first is behind what's drawn second, except for windows drawn inside the BeginWindows-EndWindows block.

In the Spaghetti Machine, the lines are displayed behind the panels because they are drawn first. Boiled down to what is relevant to your question, the OnGUI method looks like this:

public void OnGUI () 
{
    // Display links - they appear behind the panels
    foreach( EditorLink link in maLinks )
    {  
       link.DrawLink();
    }

    // Display panels
    BeginWindows();
    for( int i = 0; i < maPanels.Length; i++ )
    {
       EditorPanel panel = maPanels[i] as EditorPanel;
       panel.mWindowRect = GUI.Window( iID, panel.mWindowRect, DoPanelWindow, strTitle );
    }
    EndWindows();
}

I just made a quick test what happens when we draw the lines after EndWindows() :

public void OnGUI () 
{   
    // Display panels
    BeginWindows();
    for( int i = 0; i < maPanels.Length; i++ )
    {
       EditorPanel panel = maPanels[i] as EditorPanel;
       panel.mWindowRect = GUI.Window( iID, panel.mWindowRect, DoPanelWindow, strTitle );
    }
    EndWindows();

    // Display links - they appear in front of the panels
    foreach( EditorLink link in maLinks )
    {  
       link.DrawLink();
    }
}

In this case, the lines are actually drawn in front of the panels.