I think of it as an historical jigsaw. Academics can't fill in the gaps, but we can. We get to take sides, too. It's great! Most studies written by scholars tend to take a neutral stance over whether someone was a good or bad guy - novelists can be partisan, provided they back it up in the writing.
The thing is to spend time being as exhaustive as is humanly practical, to get as many pertinent facts as you can. Getting the event framework is easy; finding the detail about lives and how people lived is harder, depending on the time/country of study. I'm very excited because I've just received a book I ordered on what people owned in my period of interest, and what those things cost. As an extra benefit, the academic who wrote it has listed every material possession of a man who plays a minor but significant role in my novel - right down to his socks! This is because he fell foul of the ruler and had his entire estate and 'stuff' evaluated and listed. It gives me a real hang on what my characters owned and how they lived, and also such detail as the relative worth of a sum of money.
If I find a fact that turns my story around, I can't ignore it. I might try and slant it in such a way so that it works my story, but I can't reject an outright truth. Better by far to stop for a short time, absorb that fact and then let it be part of the story.
Example: My protagonist is motivated to avenge his father's framing for treason. When I started out, I had a (very schmoopy) scene where his dad taught him to ride, etc, etc - all very cutesy and cliched. I loved that scene. Unfortunately, the weight of evidence suggests my protagonist was about two years old when he last saw his father, and it's unlikely the romantic ride through the forests around Pereiaslavl happened. *sigh*. I loved that bit. So when I finally caved in, I invented a scene where the kid saw his father arrested, and was traumatised and it becomes a central mystery until he uncovers the memory as an adult. I love that bit, too, and it has no schmoop, which is a good thing, at least.
I think, though, it's the author who decides whether the evidence is compelling enough so you have to take account of it. You can weigh up the pros and cons before deciding. Sometimes, accounts of long-ago periods are suspect, or the source is not to be entirely trusted as it might be tendentious. However, if a Military Register has character X fighting in a siege in 1592, then it's probable he did. If the defecting traitor courtier writes his memoirs and insists X Monarch was a devil unhung, then you probably have greater room for manoeuvre. It depends on the source.