Actually what might be interesting is 7554, a game about the battle of Dien Bien Phu, I don't know how good the singleplayer is though but it appears to have the same gameplay as CoD.

https://en.wikipedia.org/wiki/7554

Frontlines: Fuel of War
Sadly steam only.. Definitely worth a shot though.

Yeah I suppose if you know history well enough then such inaccuracies could ruin the game for you a bit. Luckily I don't have such a detailed knowledge of the history, or familiarity with the setting, to pick up on things like that.

One historically thing that I was surprised to learn about in one of these games, came from the final mission of MoH:Airborne. I thought that that huge AA tower was simply a fictional setting to have a big shootout for the game finale, but it turns out that the nazis actually did build several of those towers in certain cities, or at least in Berlin. The size of it is a bit exaggerated though in the game I'm sure.

Star Wars Battlefront II
It takes place between war.
:P

not totally "true" on the war scenario but well closer to it than Crysis - Spec Ops the Line - http://store.steampowered.com/app/50300/ - comes to mind .
Good things about the game - can be quite challenging depending on your difficulty level choice and well the story is amazing and kinda "deep" and believable characters and you get choices during story and different endings.
The launch trailer doesn't do the games "complexity" justice but may be an option to get an basic understanding of the graphic/basic setting - https://www.youtube.com/watch?v=kIoJnMT3yUI .

Well, I recall only the first 3-4 levels were about that, the later levels of United offensive were maybe not like that but to be honest I don't remember.

Yes the Germans build flaktowers, though what they should have done was remove Goering and not stall new fighterdevelopement for 2 years between 1940 and 1942. If they hadn't the Luftwaffe could have had Me262's and Do335's available in 1943. Actually they should have removed Hitler as well.

Gamespy's shut down is the reason and since GOG did not have proper online capabilities they did not want to host a game they cannot support with online updates.