If they have their own TV rights, what happens when their opponents have their own TV rights and there is a conflict? Whose cameras will be allowed in the ground? Visiting teams contribute to the match so Liverpool cannot prevent them from having their own TV deal or should the visiting team demand half the payments received as without an opponent, Liverpool have no product to sell? Do they picture negotiating with every TV franchise in the world or would they be looking to sell exclusively to one sports channel, say ESPN for example?
The trouble with having your own TV deal is that you may find TV franchises may not include it in packages. I don't recall seeing any option for seeing live Barcelona or Real Madrid matches. Of course, the USA tends to be USA only sports centric but that's besides the point.
The only thing similar I can think of would be Notre Dame football - they have an exclusive deal with NBC for their home games so it doesn't matter who they play at home, it's on NBC. Part of that might be because they are an independent school rather than part of a conference, but I would have thought other conferences have TV deals of their own and these seem to go out of the window when one of those teams plays at ND?