First of all, the linked post is hilarious and well worth a skim, but secondly, it brings up something I've been following in GOT for a few years now which is: even if Jon Snow gets DNA evidence showing he has Targaryen blood, that does NOT mean his claim to the Iron Throne is secure. Not even close! He will still need to overcome all of the following legal issues. The reason why only the first 2-3 episodes of Season 8 will be spent in the North is because the rest of the season will be needed to deal with these legal conundrums. Vanquishing the Night King will be simple by comparison!
In most traditional royal families, the heir to the throne is not allowed to marry without the King's consent. There is no evidence that Mad King Aerys consented to Prince Rhaegar's secret marriage to Lyanna Stark. Therefore, the marriage was likely illegal and Jon is still an illegitimate Snow, NOT a Targaryen.
Even if the Mad King did consent, he may not have been legally competent to do so at the time. He was, after all, mad. There is no evidence he had a competent guardian who had been granted the authority to consent to royal marriages during the King's incapacity.
Ned Stark formally asserted paternity over Jon Snow. No one contested that claim at the time, or since. Presumably there is a statute of limitations on filing a challenge to paternity. If it has passed (as it surely has after over 20 years), there may be a legally irrebuttable presumption that Ned Stark is Jon's father.
Jon freely accepted the position of King in the North. That job traditionally requires affiliation with House Stark: "We know no King but the King in the North whose name is Stark"! Thus, Jon is collaterally estopped from claiming to be a Targaryen.
Even if Jon WAS originally a Targaryen, the original Jon is now legally dead. His body was resurrected, but the present version of Jon may be a new person, at least from a legal point of view. It's possible that any claim to be a Targaryen and/or occupy the Iron Throne died with the original Jon.
The Iron Throne is affiliated with the Faith of the Seven. Jon Snow was resurrected by a rival god, the Lord of Light, for reasons known only to that deity. Being a possible agent of a heretical god might also negate Jon's claim to the throne.
By joining the Night Watch, Jon legally renounced any claims he had to inherit his family's property or titles. The Night Watch oath states that "I shall take no wife, hold no lands, father no children. I shall wear no crowns and win no glory." Thus, Jon is specifically barred from claiming any crown. Perhaps that oath was negated by his resurrection. But if so, why isn't the original claim itself also negated, as per point 5 above? Jon can't have it both ways. If he's a new man post-resurrection for purposes of the Night Watch, he's also a new man for purposes of inheriting the throne.
Once Daenerys finds out that Jon has designs on her throne, her team of crack litigators will surely raise all these issues and more! Plenty of material for a season of Law and Order: King's Landing.
