I think -- and I've done a lot of reading on this, but it's been awhile ago and I'm a bit vague -- I think the point was that it was under Richard that the boys were declared illegitimate -- that was the basis of his claim to the throne (that Edward's marriage to Elizabeth Woodville had never been legal, so all their children were illegitimate). I don't recall if Henry Tudor ever formally stated that wasn't the case, but his whole premise in marrying Edward & Elizabeth's daughter, Elizabeth, was that they WERE legally married and all the kids WERE legitimate (because of course he wouldn't gain anything by marrying an illegitimate princess). But then her brothers would have a better claim to the throne than Henry would. So the pro-Ricardian thinking is that the person who stood the most to gain by having the boys murdered was Henry Tudor or some supporter of his, who by having them quietly killed could dispose of them as rival claimants to the throne and also pin their deaths on Richard, making him out to be a child-murderer.
It was definitely Henry who needed the boys out of the way, permanently. Richard had secured the throne, declared them illegitimate, had them safely in the Tower, and their power base was pretty much non-existent. I think Henry did revoke the Act of Attainder against Edward's heirs, because otherwise he would have had no advantage in marrying Elizabeth of York. So for him to do that, he surely had to be confident that those boys were dead.
And, as far as I'm aware, despite all the things done to sully Richard's name after his death, I don't think Henry ever accused him of murdering the princes. It's certainly possible that he did it, but it would have been a relatively needless act of brutality, I think. And regardless of what Shakespeare and other Tudor propagandists might have written, no contemporary sources ever accused Richard of being cruel or evil.
But in many of the theories I've read, it's the Duke of Buckingham who seems to be the most likely suspect. One of Richard's loyal supporters, he later betrayed Richard and joined a plot to have Henry Tudor crowned, as the only remaining Lancastrian heir (for want of a better term). It has been put forward that Buckingham did it to curry favour with Richard, or that he did it to help the Lancastrian rebellion, or that he wanted to press his own claim to be king, and needed to start whittling down the claimants.
It's sad that, for many people, this series will perhaps be the story of the Wars of the Roses, because it's a far more complex, detailed and interesting tale than can be told in a series of romance novels masquerading as history.