The Writers Focused Too Much on This Theory to Leave Us Hanging
Game of Thrones's writers foreshadow the hell out of a story when they want to, and in season five, they laid hints everywhere about this theory of who his parents are. The writers didn't reveal his true parentage by the end of the season, but they are also in the habit of thinking about the bigger picture. I still think the long game is to reveal Jon as being of royal blood, because they alluded to it so heavily. The writers regularly leave out subplots and details from the book for time and story constraints, so there would have been no need to drop those hints if they weren't going to point to something in the future.