I think I understood what you were asking and I thought you could extract some information from that video.
Let me try to clarify though.
Normally, site wide links are bad, even if its only one site to another and not the other way around. You could argue that they add value, which is why I linked to the above video, since it seems like that is a hard case to make (I don't know the site, I am just assuming).
So, this is really a bigger issue of value add. If it does add value, you could make a case that they should still be there.
That said, even in that situation where it does add value, the link should still probably be a no-follow since Google will likely interpret this as a spam signal or just simply trying to "beat" them at their game.