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I always felt so sorry for Desdemona. Her only crime was to be noble and loyal to a paranoid man-child. So, no she doesn't bring this upon herself. Iago's scheming and Othello's insecurities target the innocent Desdemona. She is largely the perfect Elizabethan wife. Shakespeare set her up this way to highlight Iago's "evilness" and Othello's many issues.
I would have to agree with you, Aslan. Desi was always just a pawn in Iago and Othello's game, and neither Othello nor Desi knew they were playing. I always wished that I could find something to throw her under the bus for, because this would have made her a far more juicy character.