In this case the rightful heir being Mary Tudor was not a "re-write" of history, or anything else. She was the daughter of Henry VIII and Catherine of Aragon, his first wife, and the sister of Edward VI, son of Henry VIII and Jane Seymour, his third wife. Henry VIII laid down his wish for the succession in his will, and Mary Tudor was the preferred successor should Edward die without issue. As this was the case then it was proper that Mary should be crowned when Edward died.
Lady Jane Grey was related to Henry VIII thus: Henry's sister Mary's second marriage to Charles Duke of Suffolk bore a daughter, Frances who married Henry Grey, Duke of Suffolk and this union produced the Lady Jane.
Now tell me in what way Lady Jane Grey was more entitled to the throne than Mary Tudor? She was pushed into the pretence of monarchy by her scheming parents and in-laws. Mary was away from London at Edward's death, and the conspirators kept the news from her and tried to ambush her on a fruitless errant on which they sent her. She suspected foul play and learned of the truth about Edward and avoided the trap, gathered loyal forces and advanced on London, where the conspirators melted into the mist leaving Lady Jane to take the fall out. See more about the family lineage here.
http://www.royal.gov.uk/files/pdf/stuarts.pdf