Re: HBO TV series sneaking in possible hints for the book series? !!! SPOILER ALERT!!
As for the prospect of a Stark being sacrificed to end the Winter and the advance of the Others....it's the best theory I've heard yet with respect to Mel's insistence that a King's blood must be sacrificed. She's tried sacrificing kings but obviously none have pleased her red god...likely because they are not true kings.
Was Robert a true king? Not really. Thus, Stannis and Renly (nor any of Robert's many many many many bastards) are not either. Certainly neither Joffrey nor Tommen are. Balon doesn't count, either.
I don't remember Mel sacrificing any "kings" and not getting results. By the power of Stannis's King's Blood (okay, well maybe not blood per se), she was able to make a shadow assassin. Who else did she sacrifice without result?
Robert Baratheon was an usurper, so it wasn't in his blood before he was crowned, but he had power enough to make his bastards valuable to Mel. I think the power of the King's blood comes from the fact that they are crowned kings, not necessarily from genetic material before their time. It's magic after all. Maybe it's the magical power that comes from their followers believing in them, or something magical about the laws of their universe that recognizes a "king".
I think the idea Tywin raises about magic recognizing the shifts in leadership of Westeros is an interesting one. We know that magic carries a fair amount of weight in Westeros, but it also seems that prior to fairly recently (red comet, dragons, etc.) that it has been a primarily dormant force south of the Wall. (There is ample evidence to illustrate the active and enduring magics the Wall has been infused with.) The only solid evidence of magic in Westeros proper are the pyromancers' mention of wildfire being manufactured much more easily and rapidly which, according to them, could not be explained by anything other than dragons existing (which they do in Essos). And of course Mel.
But with all of these magics, even in the case of Dany's dragons, there has been action and intention. Valyrian steel is spell-forged, presumably by a spell-caster. The Wall was built and infused with ancient magics by spell-casters (later called maesters) to defend the realm of men. Dany had to put her eggs on the pyre (intention and action, even if the outcome was unknown) for the magic of dragons being born into the world to occur. Lastly, Melisandre casts spells to work her magics for good or evil.
As there are no set rules or laws with which magic is defined, let alone governed, there is no qualifiable evidence to suggest that magic would define who or what a true king is unless...
We examine the magic of Westeros itself. Before the Andals and all that, there were the Children of the Forest, the Greenseers, etc. The continent of Westeros was covered with weirwoods, known as "heart trees." Somewhere along the line, the Children of the Forest carved faces into the weirwoods, which would be a way for man to connect with a spiritual force he cannot see or understand, the same way the Faith of the south has the Seven Faces of the One God (modeled after Christianity's "Holy Trinity"). Human beings as people can more easily relate to something with a face. Based on this, it could be argued that the "old gods," understood and related to by the faces in the heart trees, are the spirit or essence of Westeros itself.
The old gods are felt most deeply and best understood in a godswood, which used to cover the continent, and are still kept in the south by more prominent families (in tradition, if not in use), it could be argued then that the power of the old gods, reinforced by Bran's experiences, can be interpreted as the spirit or the essence of Westeros itself. If Westeros itself has a stake in the lines of succession, and whom it would thus recognize, there could be only one answer.
The Starks
Starks have not borne the title of king (until Robb) for many years, but who they are has never changed. The same blood, the same character, the same traditions they carried as kings define who the Starks are today. Hell even Robert said that Ned should've been the king, though Ned was right...his place was in Winterfell.
Brandon "Bran the Builder" Stark, was the founder of House Stark, first King of the North, and builder of both Winterfell and the Wall. Throughout the ages, there has always been a Stark at Winterfell (until very recently, and due strictly to circumstance) and there has always been a Stark on the Wall, both defending the realms of men.
Under the premise that a king's blood would be required to save the realm (from the Others, from its people, from anything), only the blood of a king recognized by the governing powers of the magic being invoked would do. As the current and most pressing threat to the realm is that of the Others, it stands to reason that the kingly blood recognized by Westeros would be that of the Starks.
So it makes perfect sense: If Robb, a true King, produced a legitimate male heir, it's not someone we're going to get to know particularly well (I don't think) and are not likely to be horribly attached to...apart from the fact that he may or may not represent the last of the Stark line...then he would be the best candidate for the sacrifice that Mel insists is necessary.
It does not necessarily have to be Robb's heirs. As attested by Melisandre in her desire to use Edric Storm/Gendry, the king's blood is required, which also includes direct descendants of that line. Robb was made King in the North, but he was not the first. Robb, as was his father, his father's father (you know the drill) were all descendants of Brandon Stark, first of his name. King Torrhen bent the knee to Aegon the Conqueror, removing his style as king, but that did not make him any less king's blood, because of his parentage.
So any direct descendant of King Brandon I Stark possesses king's blood. This includes Sansa, Arya, Bran, Rickon, and Jon.
As for Melisandre, while her true powers are still for the most part hidden, she doesn't have much in the way of king's blood (that of Edric Storm/Gendry) and her magic that she's responsible for. She burned some leeches. One Balon Greyjoy, one for Robb Stark, one for Joffrey Lannister-Baratheon. All three deaths occur, but not one of them is attributed to her. Balon Greyjoy either gets blown to his death by a stiff breeze, or Crow's Eye gives him a nice shove (and as far as we know, Melisandre has no involvement with the Greyjoys), Robb Stark suffers TRW, which is conspired between the Freys, the Boltons and the Lannisters (none of whom share any affiliation with Melisandre, as she's for Stannis), and there has been no evidence to suggest that she has any hand in, or any involvement with the players who conspire, the Royal Wedding. Sure, she makes the comment to the effect of "the Lord of Light chooses those necessary as instruments to bring about His work" and she could attempt to chalk it up to that, but that's no different than me *thinking* "I wish someone would beat up that bully who stole my lunch money," then go home and stab my voodoo doll made out of kleenex and duct tape, then bully gets beat up by someone else for a totally unrelated reason, and then me saying the next day, "Yeah, I beat up that bully."
It just doesn't fly.