So was the Mad King's wife also a blood Targeryan? (i.e. incest). Dany has resistance to heat, but how can she then be a Stark.... Unless, both families have been wrong all of this time and the Starks are really the Targeryans!!!
Here's what I expect: Ned was the true son of the Mad King's father, and the Mad King was actually the son of the man who Ned though was his father (i.e., Grandpa Stark). That way Jon is not a blood Targeryan because Dany's brother was also a Stark fathered by Ned, and Dany would then also be Ned's daughter and she would (in a somewhat roundabout way) be a blood Targeryan because Ned was the true Targeryan all along!!