Yun nga ang gusto nilang palabasin. If true, then Rhaegar is not so noble after all, and Lyanna is a slut and a home wrecker. And why dwell on Jon parentage? It doesn't make him any more legit to the throne. Robert is the last king, that means Gendry should be next in line.
Jon is King in the North not because he is a Stark. He doesn't need to be Targaryen to be King of the Andals.