The short answer is yes and no.
Yeah, I didn't think that would cut it either, so here is the long answer. Bear with me a moment.
You need to be well versed in history as it applies to the setting you will use, and only the setting you will use. This will be modified by the level of magic you allow into your game. For example, if you set your game in ancient Greece, or Egypt, all you really have to concern yourself with is the basic (and I stress this) religion, events, locations, and major personalities (read NPCs) of the time period you plan to use. This reduces the amount of precious time you have to setting and gets you into what you want to do in the first place, gaming. If, however, you allow magic that traverse time (chronomancy) or place (teleport, teleport without error), then you should at least have some inkling on the culture that the PC's end up in.
But Greystoke, you ask, how can I be sure the PC's will choose to go to another culture/time that I have prepared ahead of time? That, my friends leads me to the 'No' part of my answer.
The key to this scenario is to control the magic and be aware of the possibility before hand. For example, if you only have time or desire to bone up on Ancient Greece, then limit the spells that permit the traveling of vast distances. For this example, there are plenty of mysterious city states and islands around the Mediterranean, so entire campaigns can be played there without leaving it.
Secondly, this game is fiction to begin with, so an accurate accounting of history in all areas is not necessary. If it were, there would be no magic to being with! With that in mind, if your PCs do happen to wander away from a area you have prepared there is no problem with them encountering a tribe or society ( or race for that matter) that has no historical record.
Of course, adding magic to a culture from our history should have some ramifications that you should consider, but we will get to that in another post.
My first point is how little this article appears to contribute to running a historical campaign. All I walked away with is; (a) be well prepared by fleshing out your setting ahead of time, and (b) don't let your players wander into areas that you're not prepared for.
While no two DMs are the same, I can say that the cream of the crop which I have had the pleasure of gaming with were at their best when they had to think on their feet because the players did something unexpected, be it an innovative idea, killing off an important NPC, ignoring an "important" plot point, or going someplace the DM didn't expect them to go.
I always find myself cringing slightly when someone posts here on the boards that the answer to "what if the PCs try to do [X]" is "take away and/or limit their ability to do that". Why isn't the answer "Hey guys, I want to do [X] and it would would be a big help if you didn't try to teleport halfway across the world". Heck, if your players are cool with it, limiting their abilities can be an option, but I personally don't think it should ever be the first choice.
My second point is minor, but I feel that constructive criticism can be helpful.
The structure of this article makes it a little difficult to read, and there are grammatical mistakes. Were this anywhere else on the boards I wouldn't bother to bring it up. However, since this is Regdar's I would expect the quality to be held to a higher standard.
I'm still not quite sure how the answer to "how well versed in history do you have to be..." is "yes and no". It's not a yes or no question.
While the subject matter is interesting, thus far it hasn't delivered anything to help DMs who are looking to incorporate history into their games, (granted it's only the first in what I expect to be many posts).
Just my
I find that historical knowledge helps immensely when putting together settings, and it does interfere with my enjoyment of my friend's other settings, particularly when they set things in the 'real world'.
For example, in my friend's setting, Beijing is a coastal city. As you can see on any map, it is fundamentally not. This arose because of complete lack of knowledge of the city, not really any 'world shaping event'.
I also incorporated my historical knowledge into my main setting "Alliances", a setting themed after medieval Imperial China. It definitely helped in the inspiration of NPCs that followed the setting and not creating 'dissonance'. Also it's a wonderful source for ideas, and a check for not being redundant. It gives you ideas for planning and structure and a 'realistic' idea of how things should occur.
However, it does detract from enjoyment a little, as many adventure ideas do become predictable, as many DMs are following on historical threads picked up by fantasy authors, TV or what have you.
In any case, history provides a varied array of personalities, costumes, settings, and situations. And it's often obscure enough that people won't pick up on it. Tip? Open up a book, pick a topic, and transplant it to D&D. Usually you'll get something interesting, and unless you've got another history buff in the house, you can often surprise other players.