It hardly matters about the legitimacy of Edward IV, (And his daughter Elizabeth of York, who married Henry VII (Tudor)). Henry Tudor, of dubious lineage himself, claimed the throne by right of conquest, not really by blood. After all, the Lancastrian/York dispute began because the Lancastrians claimed that descent could not go through a woman, yet Henry's claim to the throne was through his mother. So his real claim was that he won the battle of Bosworth, defeating Richard lll. That he later married Elizabeth was a bonus, and a peacemaking gesture- but the legitimacy of her father would have had no bearing on his right to the throne- he was king regnant- she merely his consort. Had he remarried after her death, and there is evidence that he considered it- his children by his second wife would have had equal claim to the throne as their elder siblings', regardless of their mother.
Likewise, whoever is the lineal claimant of the Stuarts, (someone on Lichtenstein, I believe?), it hardly matters, since parliament has called on and chosen the descendants of Sophia, grand-daughter of James l. They have been accepted, crowned, and thus have been the true sovereigns for 300 years now. A few attempts to overthrow the Hanoverians failed- the pretenders did not have enough support among the British people. A "claim" doesn't matter, reality does. Of course, tracking alternate lines of succession may be of interest to genealogists, and can be fascinating- but are those marriages and parentages studied as closely as the ruling lines? I'm sure that there are a few dubious marriages/offspring in those lines too- they just aren't studied as closely.
Anyone claiming to be the "true Monarch" has to remember that since 1066, the line of England/Britain has been descended from a conqueror too- surely one has to go back farther than that and find the true monarch through the Saxon line! If one can't accept Henry Vll's claim, one can hardly accept William l's!
