Who were the rightful holders?
Edward was born April 28th, 1442- and while there's no reason to say he couldn't have been prematurely born (though that would seem to have been something they would have noted because of risks to true claims to the throne) the 9 months back from that puts Edward being conceived when his “father” was not there at all. Edward's christening was a hushed up affair, and Edward looked nothing like his supposed father, and his own mother swore in a legal deposition Edward was a bastard. Following the War of the Roses, the only claimant left was Henry the VII who married Edward the IVth’s daughter Elizabeth of York.
The entire descent from this thin claim to the throne, including Henry the VIII is posited to be illegitimate, all the way to the Windsors, and the current queen. Of course Edward IV could have still claimed the throne by right of conquest. If all of the above were proven then the line of monarchy should have extended the Plantagenets. Henry VIII made sure the only surviving Plantagenet, Margaret Duchess of Salisbury was executed (Edward Earl of Warwick died locked away in the Tower previously) and so the line died out, as far at the throne from there on.
The actor who played baldrich on Black Adder did an intriguing BBC documentary of interest: http://www.youtube.com/watch?v=eF2YaQgJwH8
This is all well and good....but who the heck cares in the USA, where we long ago renounced ANY king of England. And certainly not king obamaumao of the US