I did graduate work focusing on anachronism in Medieval and Early Modern European thought, so it's actually one of the things that fascinates me about D&D.
I'll agree as long as by "some respects" we mean a very few respects. Fundamentally, outside of the more familiar elements of material culture, these settings have nothing really to do with either era. And fundamentally even enthusiasts of these periods tend to have a very shaky understanding of them so it couldn't really be any other way. Even if the settings were designed by medieval studies PhDs almost no players and DMs would actually run it true to the era.
The difficulties in trying to run an "authentically" mediaeval RPG are almost insuperable, I think.
Even if one overcomes the problem of working out what is the truth about the mediaeval period - itself the subject of dispute among those best-educated in the field - there is what I think is an even bigger problem in the RPG context, namely,
outlook and
motivation. Both my own play experiences, and reading others on these boards, make me think that very few RPGers want, or are able, to play characters whose outlook is not modern. One sees this most starkly, but not at all exclusively, in discussions of paladins and alignment where behaviour that falls broadly within the romantic/honourable self-conception of a mediaeval warrior is labelld as "lawful stupid".
I'm currently most of the way through the second volume of Runciman's three-volume history of the crusades. Any expert mediaevalist probably has views on the correctness of its approach and account; I'm not qualified in that respect. But he has a lot of footnotes to primary sources and so I assume that the basic recount is largely accurate. Here is one story he tells, loosely summarised:
In the mid-twelfth century a Frankish army is on campaign against Nur ad-Din. They encounter some soldiers whom they take to be scouts, but they then realise they've encountered Nur ad-Din's main force. This is because they hear the whinny of a mule which had been a gift from the Franks to a sheikh whom they knew to be riding with Nur ad-Din in his army - per Runciman, the mule whinnied because it recognised the smell of the Frankish horses that it used to hang out with.
When one starts to extrapolate from this story to everything it implies about social and political relationships, the apparent lack of correlation between personal affiliations and loyalties on the one hand and "political" ones on the other, gift-giving between ostensible enemies, etc, one gets glimpses of a world which no D&D game I'm aware of has ever emulated.
How often in the history of D&D play has a party of PCs found itself fighting someone riding a steed that was a gift from the PCs, and this
isn't a sign of betrayal, or of some fundamental change in loyalties (eg Kitiara in Dragolance), but is just what one expects, because duty (which everyone acknowledges to have almost overwhelming importance) brings acquaintances, even friends and allies, into conflict?
