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I think you're overlooking the fact that Edward IV made Richard Protector of the country should he die before his son reached his majority. Elizabeth Woodville staged a coup - her son, Dorset by husband #1, ransacked the treasury and news was delayed to Richard (living in the North) that his brother, the King has passed. When Richard marched toward London, he did so, unarmed with a small entourage, leaving his own Middleham Castle undefended. His entourage was attacked by Dorset. Richard and his mourning party was not even allowed to enter London in peace.

What happened next - we know, but not why. Evidence was brought to Richard that Edward's marriage to Elizabeth was invalid, and the marriage was declared null and void. We do not know if Richard believed it, or if it was a legal maneuver made in panic because of Elizabeth's failed coup.

What happened to the boys is pure speculation. We simply do not know. We know that Elizabeth Woodville sought sanctuary after her marriage was declared invalid and after the boys disappeared, and that Richard publicly asked her to leave sanctuary and promised her a pension if she did so. She left sanctuary, was not mistreated. Richard kept his word. By contrast, her treatment by Henry VII was much worse!

Richard's actions probably would have been totally different had he been allowed to enter London as a mourner, if Elizabeth had not staged a coup and if Dorset had allowed him to mourn in peace. We know Richard hated London, and loved living in the north.

Nobody knows exactly what happened to the boys, but why in 1483, with speculation mounting that the Princes had been murdered, did he not produce them? The simple fact is that as long as they were alive, his claim to the throne was extremely dubious. Nevertheless, if he could have produced them, it might have stemmed the died of people defecting to Henry Tudor or dropping their support for Richard.
The simplest and most reasonable assumption is that the Princes were murdered some time in 1483 to secure Richard III’s hold over the throne.
The most charitable plausible scenario is that they died of natural causes... at the same time...