As a matter of evidence, and in order to alleviate the suffering (because I firmly believe that if you look to history to match your pain, even if the world is historically shitty, somehow the familiarity is comforting) I present to you -- via the blog of writer (and self-proclaimed nerd) Ted Gideonse, other movies which won Best Picture over better movies:
1) Rocky over Network, All the President's Men and Taxi Driver.
2) A Man for All Seasons over Who's Afraid of Virginia Woolf?
3) Forrest Gump over Pulp Fiction.
4) Dances with Wolves over Goodfellas.
5) A Beautiful Mind over LOTR: Fellowship of the Ring.
6) How Green was My Valley over Citizen Kane.
7) An American in Paris over A Streetcar Named Desire.
8) Gladiator over Traffic and Crouching Tiger, Hidden Dragon.