I expected Tudor propaganda simply because everyone thinks Richard was such a terrible person, and there wasn't any lengthy biography of him written before Shakespeare wrote his play, so that must be where the impression of him came from. I don't blame them; certainly Richard was a ruthless man, and they would have wanted to cement the basis of Henry VII's rule as something guided by God, rather than a lucky Welshman who happened to be able to collect a lot of people who didn't like the unpopular king, and was able to kill him on Bosworth Field.
To understand why the Tudors wanted Henry VII to be seen as the start of this Godly dynasty, you have to go back and have some understanding of the Wars of the Roses. If you really want to get picky about it, you go back to Agincourt, the high point of England's successes in France. Henry V seemed unstoppable in France, and it seemed as if the Norman Conquest of 1066 might finally be avenged 350 years later. Had Henry not died when he did, maybe the French would all be speaking English and would have bad teeth nowdays.
But Henry V died, and his son Henry VI was a minor. He wasn't a strong guy, and he got pulled in lots of directions, depending on who was talking to him at the moment. He wound up losing most of the gains of his father (by the time of the Tudors, 60 years later, all that remained of the great dream of England taking France was Calais, a little fort directly across the English channel).
So Henry VI marries Margaret of Anjou. She's a willful high strung French girl who really doesn't like England, and doesn't care who knows about it. So here's this really powerful woman (who may or may not have had her son via adultery) married to this simpering dolt of an idiot husband who has spells of insanity, is losing land left and right, and is more interested in praying than being a husband to her. She's been Queen Consort since she was 15 years old, she's stuck in a country she hates, and she's rash and takes way too many chances.
Given her husband's incompetence, some people start talking about rebelling. One of those people is Richard, Duke of York. He talks openly. In fact, he has Henry VI declared insane, and he gets himself named the Lord Protector. He even had an agreement drawn up saying that he would become King after Henry VI died. But then he himself died before he had any chance of pressing his case. Interestingly enough, he's the father of Richard III. So, you know, the apple doesn't fall far from the tree.
Ok, so all of this winds up leading to the Wars of the Roses, whereby the House of Lancaster (Margaret of Anjou, Henry VI, their family) fight the house of York (Richard, Duke of York, and his family). There weren't really a lot of battles, most notably Tewkesbury and Barnet, but it did consume people for a generation, and England's economy continued to fail while all the nobles were busy killing each other.
So the Tudors come out of this from left field. Way back when Henry V dies, his widow, Catherine of Valois, marries a squire in her court, Owen Tudor. This is Henry VII's grandfather and the great Queen Elizabeth I's great great grandfather - a squire at court. Catherine and Owen had more children together; half-siblings of the house of Lancaster. Henry VI had them recognized as legitimate as an act of kindness to them, and tried to bring the blended family together. So the Tudors get their royal lineage on their mother's side, and it's fairly tenuous as well, but they start to rise through the ranks of the nobility, and by the time of Richard III, Henry Tudor was seen as a real threat to the Yorkist, and was hiding in the Netherlands or Brittany or somewhere across the Channel.
Richard III was the brother of Edward IV, who was Richard Duke of York's son (and Richard III's brother). He wound up winning the title of King by fighting for it, and had the Lord Mayor of London proclaim him King while Henry VI was far away from the city. The whole thing was really messy.
Edward dies suddenly in 1483 and all hell breaks loose. His children are still minors, and his brother, the future Richard III, is supposed to protect them until they reach the age of majority. Instead, they disappear and Richard becomes King. Yeah, he probably murdered them. It was so much more convenient than simply asking them nicely to step aside.
Richard III becomes King, no one really bats too many eyelashes at the missing Princes (except for their mother, of course), and life seems to go on as normal. But then in 1485, Henry Tudor, not content to let Richard pull this charade, decides that he's going to be King, and he sails from wherever it was he was hiding (Brittany, France, Luxembourg, somewhere) with an army he raised, and he lands in Wales, gathering support as he moves through the countryside. A bunch of Richard's allies, fed up with his hubris, and smart enough to see which way the wind is blowing, switch sides.
Henry beats Richard at the Battle of Bosworth Field, and declares himself King. He marries a Yorkist woman to unite the two rival houses, and he really wants to reign peacefully for a long time. Unfortunately his first son Arthur dies as a teenager (he was named Arthur after the great legendary King, and it shows how much Henry hoped to start a new golden age) and his younger brother Henry, who'd been studying with monks up until now, suddenly has to be groomed to be King.
And then of course Henry the Younger has lots of marriage problems that go on for decades, and each of his three children take turns with the throne, young Edward a disaster, Mary I an even bigger disaster, and then Elizabeth, who refused to marry because she probably had some pretty deep psychological trust issues given her history. So she never had an heir, and never named one.
All in all, when Richard III was written, just after the trouncing of the Spanish Armada, things were looking pretty good for Elizabeth, and the Tudor story. But everyone also knew that the Tudors were probably going to end with Elizabeth, since she had no children. So they wanted to showcase just how awesome the Tudors had been, and make a case for their having taken the throne in the first place, so that after Elizabeth, people wouldn't talk shit about the grandchildren of squires being too big for their britches and becoming King illegitimately. Mostly, they also wanted to avoid another Wars of the Roses, and make everyone remember just how awful some of the monarchs were back then, especially the monarchs who were on the other side of the Tudors.
So given that history, I'm not surprised that in his opening monologue, Richard goes on about how disfigured he is (he wasn't too much, really - his skeleton shows he had scoliosis and had some curvature in his spine, but he was still well enough to wear armor, no small feat, and fight in battle) and how he scares dogs and children. He proposes to a woman whose husband he had killed. He does all sorts of nasty things. I'm pretty sure no one who gets to be King is that publicly ruthless before he's King. Maybe after, but not before.
I'm definitely not joining the Richard III society any time soon, and I'm not really a huge Ricardian, but I do see where they're coming from - Richard wasn't any worse than anyone else from the time, and others did the same sorts of things he did.
Not according to Shakespeare, though. But that's why the victors get to write the history books. And the history plays.