OK, follow me on this one. We're starting with: "Thus, you cannot put into play or take control of a unique card which you already own or control (except for duplicates, see below)."
So, a straight reading of this says that if Player A controls a copy of a unique card in play, Player A cannot play (etc.) another copy of the same card, except as a dupe. It also says that if Player A owns a copy of a unique card that Player B controls, Player A cannot play (etc.) another copy. Owning 2 copies of the same unique card in play at the same time, even if they are not controlled by the same person, would be an illegal result, right?
Well, the Breaking and Entering situation is doing neither of those. With the Breaking and Entering situation, Player B is playing (etc.) a copy of a unique card that Player A owns while Player A owns and controls another copy. This is not, looking just at the words, in violation of the "Thus, you (in this case, Player B) cannot put into play or take control of a unique card which you (also Player B) already own or control" text. Player B neither owns nor controls a copy of the unique card that he is putting into play, so there is no violation in the resolution itself. It does, however, end up with the same illegal result (Player A owning 2 copies of the same unique card in play at the same time, even though they are not controlled by the same person) as in the forbidden sequence where Player A played the card, lost control, and then wanted to play another copy.
So, it is not Player B putting the card into play that is the violation here. The violation is the end result - namely Player A owning 2 copies in play, even though they are controlled by different people - rather than the effects that achieved it. Effectively, Breaking and Entering allows you to use legal means to "back into" an illegal result. And the ruling we just got says that said illegal result cannot stand.
So turn now to the next clause: "You also may not play or take control of a unique card if there is a copy of that card in your dead pile, or if your opponent has taken control of another copy of that unique card from you."
Again, if you have a copy of a unique card in your dead pile, you cannot play another copy. That would lead to an illegal result, right? Well, there are combinations of card effects (like the Hills) that can resolve perfectly legally, creating that same illegal result. That's the same problem, isn't it? That you can use legal means to "back into" an illegal result.
So why are we forbidden to use legal means to achieve one illegal result (Breaking and Entering), but there is no problem using legal means to achieve a different illegal result (Hills to dead pile)? Either both illegal results are forbidden, or both are allowed - and we know one of them is forbidden.