Det är generellt svårt att bevisa en negativ. AFAIK, det finns inget sätt att helt utesluta R + L = J. Det enda sättet är att titta på argument som stöder påståendet att Ned Stark verkligen är Jons far. Och dessa argument har sammanfattats i frågan du har citerat:
Reasons to affirm that Eddard is Jon's father:
In the aforementioned investigation by Catelyn, a recurring rumor was that the mother was Ashara Dayne. It is implied by other flashbacks (principally the story of the Knight of the Laughing Tree) that Ashara and Eddard shared a mutual attraction.
When pressed by Robert, Eddard claims the mother is a servant girl named Wylla. Edric Dayne claims to Arya Stark that Wylla was his wet nurse (making him Jon's milk brother), giving more credence to the story, and that Wylla was not just a name Eddard made up to shut people up.