An evil fairy almost made me include 'supposed', 'bigamous' or 'purported' in that title. After all, in a world where at least one author has put Richard III in inverted commas, I feel one is entitled to be equally catty. But I shall rise above it, and wait for an opportunity to write 'Henry IV' or 'Henry VII' when describing the said personages,
As Susan Higginbotham has pointed out there can be no absolute certainty that the traditional date for the wedding 1st May 1464 is in fact the correct one. The facts Susan produces indicate that at the least Edward was playing his cards so close to his chest that not even William Hastings knew the full SP. And if William Hastings, as Lord Chamberlain and supposed best buddy was kept out of the loop, who was left in it?
Given that medieval kings and queens lived their lives literally surrounded by attendants, it almost beggars belief that Edward was able to slip away long enough to court, win and marry Elizabeth without anyone knowing. (If he did indeed manage this feat, it demonstrates that he could have done the same with someone else, doesn't it? And we wonder about lack of proof?)
Now, of course, attendants on royal personages learn to be discreet, especially when the royal personage concerned is a young sovereign 'taking his leisure' with one lady or another. That almost goes without saying. But if Hastings really did not know, then discretion was really taken to extremes in this case. To an almost mind-boggling degree.
One possibility is that Hastings was not at court at the relevant time. Although as King's Chamberlain he was expected to hang around Edward most of the time, he naturally had his own private affairs to attend to (and indeed duties connected with his other offices), and there was a deputy to take his place when he was absent. This is something that detailed research as to Hastings whereabouts (compared to those of Edward IV) might bear dividends. But one of Hastings' key qualities was what we now call 'people-skills'. He was well-liked, and well-connected to all manner of influential people. It would be astounding if one or other of his underlings at court had not informed him of such an important development as the King's marriage.
So, on the face of it, Edward married Elizabeth and no one at court knew. It was that tight a secret. Or if someone did know, that person kept his mouth firmly shut, out of fear or loyalty.