Historical "fiction"

I love reading historical fiction. Lately I've been obsessed with Sharan Newman's Catherine LeVendeur series and C.J. Sansom's Matthew Shardlake series. I love the books a hell of a lot - they're drastically different beyond both being historical mysteries but I strongly recommend both series. Anyways, I love reading historical fiction because I love history and also because, if I had the discipline and focus to write a book, I'd want to write historical fiction. In both of these series the main fictional characters interact heavily with real historical figures. This led me to the issue of, how important is it to rely heavily on historical characters? Or for that matter, historical accuracy? Like, it's one thing to build your book around popular (of that historical period) controversies swirling around a major historical figure, but how strictly do you stick to the facts? Will your readers be happy if you invent a character to be Abelard's protege or Cromwell's steward? I kept turning this question over when I was thinking about how to build a story around characters - are you hindered by history? Or can you embrace the time but not all the minute details (does it matter if Cromwell's steward is not the same character you create in your book?) I guess I don't really have an answer but I feel like I would lean heavily for "creative application of history" as I call it - being faithful to the times yet not constrained by fact. Cromwell's steward could be whomever you want as long as the steward is not a pregnant African lesbian who believes in Kaballah. Not that there is anything wrong with any of those things, there just weren't many of either of them in England five hundred or so years ago.