I'm not sure that Thomas More is that reliable as he would only have been 7 years old at the time of the battle of Bosworth! He was certainly relating/slanting these events for the benefit of the Tudor kings to shore up their tenuous claim to the crown, and quieten any dissenting voices. As for the Princes, I find it hard to believe that Richard was totally unaware of their fate, but it certainly suited a number of ambitious people that they had 'disappeared' including Henry Tudor! Illegitimacy could be reversed as was the case with the Prince's sister/s in order for Henry to marry Elizabeth! So if they had lived, insurrection would have been a constant threat whoever was on the throne, so, like poor Jane Grey, they had, like her, perhaps regretfully, to be permanently removed. Why their bodies weren't produced under the pretext of natural death, common enough in those days, which would have taken the onus off Richard IS a mystery! The bodies were supposed to have been moved after their original disposal, so perhaps Richard simply didn't know where they were, lost without trace so to speak! If Henry Tudor found the alive and had them murdered, why did he get so hung up over Perkin Warbeck, as he would have known he was an imposter?! This would indicate that there was no sign of them after Bosworth, so back to Richard, and the mysteries deepens!!