The helicopter crash is a good example. The heroic, patriotic, and slightly comedic Marines go back for a wounded comrade, and then...their entire squad dies in a nuclear blast because they didn't evac quickly enough. Or the plucky SAS seize the only man who can give them the intel they're after, and then...commit a war crime and torture him, which turns out to be pointless when they get the information from another source anyway, so they commit another war crime and execute him in cold blood. The helicopter scene was genuinely shocking at the time, even though tragically killing off your heroes in the middle of the game is widespread today.
I felt the original Modern Warfare was the only Call of Duty that married the horrors of war from the first two games[0] to the Tom Clancy action of the later ones. Black Ops seemed more jingoistic and less willing to make the player uncomfortable, while in later games missions like No Russian that were meant to shock the player didn't combine it with anything philosophically unsettling (like the idea that "no man left behind" might get a much larger number of people killed).
That being said, I think a lot of what I got out of the game was due to where I was in life when I first played it, so it might just be sentiment tinting my memories.
[0] We don't mention 3.